Professor Guoyin Li

Professor

I received my Ph.D from The Chinese University of Hong Kong in Dec. 2007.

Science

School of Mathematics & Statistics

I received my Ph.D from The Chinese University of Hong Kong in Dec. 2007. I am currently a professor in the School of Mathematics and Statistics at University of New South Wales. I was awarded an Australian Research Council Future Fellowship (for mid-career researchers) during 2014-2018. My area of interest is optimisation, variational analysis and tensor computations. For some of my recent research articles, please see web.maths.unsw.edu.au/~gyli/papers/articles.html

Phone

9385 7095

E-mail

g.li@unsw.edu.au

Location

School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 2082

Book Chapters | 2010

Jeyakumar V; Lee G; Li G, 2010, 'Global Optimality Conditions for Classes of Non-convexMulti-objective Quadratic Optimization Problems', in Burachik RS; Yao J-C (ed.), Springer Optimization and Its Applications, Vol 47, edn. Springer Series in Optimization and Its Applications, Springer, Natl Sun Yat-Sen Univ, Dept Appl Math, Kaohsiung, TAIWAN, pp. 177 - 186, http://dx.doi.org/10.1007/978-1-4419-0437-9_9
Journal articles | 2023

Boţ RI; Dao MN; Li G, 2023, 'Inertial Proximal Block Coordinate Method for a Class of Nonsmooth Sum-of-Ratios Optimization Problems', SIAM Journal on Optimization, 33, pp. 361 - 393, http://dx.doi.org/10.1137/22m1472000

Journal articles | 2023

Jeyakumar V; Li G; Woolnough D; Wu H, 2023, 'Affinely adjustable robust optimization for radiation therapy under evolving data uncertainty via semi-definite programming', Optimization, http://dx.doi.org/10.1080/02331934.2023.2178848

Journal articles | 2023

Pham TN; Dao MN; Shah R; Sultanova N; Li G; Islam S, 2023, 'A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems', Numerical Algorithms, http://dx.doi.org/10.1007/s11075-023-01554-5

Journal articles | 2023

Zhang Y; Li G; Pong TK; Xu S, 2023, 'Retraction-based first-order feasible methods for difference-of-convex programs with smooth inequality and simple geometric constraints', Advances in Computational Mathematics, 49, http://dx.doi.org/10.1007/s10444-022-10002-2

Journal articles | 2022

Bello-Cruz Y; Li G; Nghia TTA, 2022, 'Quadratic Growth Conditions and Uniqueness of Optimal Solution to Lasso', Journal of Optimization Theory and Applications, 194, pp. 167 - 190, http://dx.doi.org/10.1007/s10957-022-02013-2

Journal articles | 2022

Bot RI; Dao MN; Li G, 2022, 'Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs', Mathematics of Operations Research, 47, pp. 2415 - 2443, http://dx.doi.org/10.1287/moor.2021.1214

Journal articles | 2022

Chuong TD; Jeyakumar V; Li G; Woolnough D, 2022, 'Exact dual semi-definite programs for affinely adjustable robust SOS-convex polynomial optimization problems', Optimization, 71, pp. 3539 - 3569, http://dx.doi.org/10.1080/02331934.2021.1902521

Journal articles | 2022

Goberna MA; Jeyakumar V; Li G; Vicente-Pérez J, 2022, 'The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments', European Journal of Operational Research, 296, pp. 749 - 763, http://dx.doi.org/10.1016/j.ejor.2021.04.035

Journal articles | 2022

Jeyakumar V; Lee JH; Lee GM; Li G; Woolnough D, 2022, 'Sums of Squares Polynomial Program Reformulations for Adjustable Robust Linear Optimization Problems with Separable Polynomial Decision Rules', Set-Valued and Variational Analysis, 30, pp. 1363 - 1380, http://dx.doi.org/10.1007/s11228-022-00648-x

Journal articles | 2022

Wang Q; Feng Y; Wu D; Li G; Liu Z; Gao W, 2022, 'Polymorphic uncertainty quantification for engineering structures via a hyperplane modelling technique', Computer Methods in Applied Mechanics and Engineering, 398, http://dx.doi.org/10.1016/j.cma.2022.115250

Journal articles | 2022

Wang Q; Feng Y; Wu D; Yang C; Yu Y; Li G; Beer M; Gao W, 2022, 'Polyphase uncertainty analysis through virtual modelling technique', Mechanical Systems and Signal Processing, 162, http://dx.doi.org/10.1016/j.ymssp.2021.108013

Journal articles | 2022

Woolnough D; Jeyakumar N; Li G; Loy CT; Jeyakumar V, 2022, 'Robust Optimization and Data Classification for Characterization of Huntington Disease Onset via Duality Methods', Journal of Optimization Theory and Applications, 193, pp. 649 - 675, http://dx.doi.org/10.1007/s10957-021-01835-w

Journal articles | 2022

Yu P; Li G; Pong TK, 2022, 'Kurdyka–Łojasiewicz Exponent via Inf-projection', Foundations of Computational Mathematics, 22, pp. 1171 - 1217, http://dx.doi.org/10.1007/s10208-021-09528-6

Journal articles | 2021

Bello-Cruz Y; Li G; Nghia TTA, 2021, 'On the Linear Convergence of Forward–Backward Splitting Method: Part I—Convergence Analysis', Journal of Optimization Theory and Applications, 188, pp. 378 - 401, http://dx.doi.org/10.1007/s10957-020-01787-7

Journal articles | 2021

Chuong TD; Jeyakumar V; Li G; Woolnough D, 2021, 'Exact SDP reformulations of adjustable robust linear programs with box uncertainties under separable quadratic decision rules via SOS representations of non-negativity', Journal of Global Optimization, 81, pp. 1095 - 1117, http://dx.doi.org/10.1007/s10898-021-01050-x

Journal articles | 2021

Goberna MA; Jeyakumar V; Li G, 2021, 'Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semi-definite Programs', Journal of Optimization Theory and Applications, 189, pp. 597 - 622, http://dx.doi.org/10.1007/s10957-021-01846-7

Journal articles | 2021

Hu S; Li G, 2021, 'B -subdifferentials of the projection onto the matrix simplex', Computational Optimization and Applications, 80, pp. 915 - 941, http://dx.doi.org/10.1007/s10589-021-00316-0

Journal articles | 2021

Jeyakumar V; Li G; Woolnough D, 2021, 'Quadratically adjustable robust linear optimization with inexact data via generalized S-lemma: Exact second-order cone program reformulations', EURO Journal on Computational Optimization, 9, http://dx.doi.org/10.1016/j.ejco.2021.100019

Journal articles | 2021

Wang Q; Wu D; Li G; Gao W, 2021, 'A virtual model architecture for engineering structures with Twin Extended Support Vector Regression (T-X-SVR) method', Computer Methods in Applied Mechanics and Engineering, 386, http://dx.doi.org/10.1016/j.cma.2021.114121

Journal articles | 2021

Woolnough D; Jeyakumar V; Li G, 2021, 'Exact conic programming reformulations of two-stage adjustable robust linear programs with new quadratic decision rules', Optimization Letters, 15, pp. 25 - 44, http://dx.doi.org/10.1007/s11590-020-01595-y

Journal articles | 2020

Burachik RS; Li G, 2020, 'Introduction', Springer Proceedings in Mathematics and Statistics, 313, pp. 3 - 5, http://dx.doi.org/10.1007/978-3-030-36568-4_1

Journal articles | 2020

Chieu NH; Jeyakumar V; Li G, 2020, 'Convexifiability of continuous and discrete nonnegative quadratic programs for gap-free duality', EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 280, pp. 441 - 452, http://dx.doi.org/10.1016/j.ejor.2019.08.009

Journal articles | 2019

Chieu NH; Chuong TD; Jeyakumar V; Li G, 2019, 'A copositive Farkas lemma and minimally exact conic relaxations for robust quadratic optimization with binary and quadratic constraints', Operations Research Letters, 47, pp. 530 - 536, http://dx.doi.org/10.1016/j.orl.2019.09.013

Journal articles | 2019

Chuong TD; Jeyakumar V; Li G, 2019, 'A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs', Journal of Global Optimization, 75, pp. 885 - 919, http://dx.doi.org/10.1007/s10898-019-00831-9

Journal articles | 2019

Feng J; Li Q; Sofi A; Li G; Wu D; Gao W, 2019, 'Uncertain Structural Free Vibration Analysis with Non-Probabilistic Spatially Varying Parameters', ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 5, http://dx.doi.org/10.1115/1.4041501

Journal articles | 2019

Feng J; Liu L; Wu D; Li G; Beer M; Gao W, 2019, 'Dynamic reliability analysis using the extended support vector regression (X-SVR)', Mechanical Systems and Signal Processing, 126, pp. 368 - 391, http://dx.doi.org/10.1016/j.ymssp.2019.02.027

Journal articles | 2019

Liu Z; Yang C; Gao W; Wu D; Li G, 2019, 'Nonlinear behaviour and stability of functionally graded porous arches with graphene platelets reinforcements', International Journal of Engineering Science, 137, pp. 37 - 56, http://dx.doi.org/10.1016/j.ijengsci.2018.12.003

Journal articles | 2019

Tang C; Jian J; Li G, 2019, 'A proximal-projection partial bundle method for convex constrained minimax problems', Journal of Industrial and Management Optimization, 15, pp. 757 - 774, http://dx.doi.org/10.3934/jimo.2018069

Journal articles | 2018

Bomze IM; Jeyakumar V; Li G, 2018, 'Extended trust-region problems with one or two balls: exact copositive and Lagrangian relaxations', Journal of Global Optimization, 71, pp. 551 - 569, http://dx.doi.org/10.1007/s10898-018-0607-4

Journal articles | 2018

Chen H; Chen Y; Li G; Qi L, 2018, 'A semidefinite program approach for computing the maximum eigenvalue of a class of structured tensors and its applications in hypergraphs and copositivity test', Numerical Linear Algebra with Applications, 25, http://dx.doi.org/10.1002/nla.2125

Journal articles | 2018

Chieu NH; Feng JW; Gao W; Li G; Wu D, 2018, 'SOS-Convex Semialgebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization', Set-Valued and Variational Analysis, 26, pp. 305 - 326, http://dx.doi.org/10.1007/s11228-017-0456-1

Journal articles | 2018

Chieu NH; Jeyakumar V; Li G; Mohebi H, 2018, 'Constraint qualifications for convex optimization without convexity of constraints : New connections and applications to best approximation', European Journal of Operational Research, 265, pp. 19 - 25, http://dx.doi.org/10.1016/j.ejor.2017.07.038

Journal articles | 2018

Feng J; Wu D; Gao W; Li G, 2018, 'Hybrid uncertain natural frequency analysis for structures with random and interval fields', Computer Methods in Applied Mechanics and Engineering, 328, pp. 365 - 389, http://dx.doi.org/10.1016/j.cma.2017.09.004

Journal articles | 2018

Goberna MA; Jeyakumar V; Li G; Vicente-Pérez J, 2018, 'Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs', European Journal of Operational Research, 270, pp. 40 - 50, http://dx.doi.org/10.1016/j.ejor.2018.03.018

Journal articles | 2018

Hu S; Li G, 2018, 'Convergence rate analysis for the higher order power method in best rank one approximations of tensors', Numerische Mathematik, 140, pp. 993 - 1031, http://dx.doi.org/10.1007/s00211-018-0981-3

Journal articles | 2018

Jeyakumar V; Li G, 2018, 'Exact second-order cone programming relaxations for some nonconvex minimax quadratic optimization problems', SIAM Journal on Optimization, 28, pp. 760 - 787, http://dx.doi.org/10.1137/16M1058480

Journal articles | 2018

Li G; Mordukhovich BS; Nghia TTA; Phạm TS, 2018, 'Error bounds for parametric polynomial systems with applications to higher-order stability analysis and convergence rates', Mathematical Programming, 168, pp. 313 - 346, http://dx.doi.org/10.1007/s10107-016-1014-6

Journal articles | 2018

Li G; Pong TK, 2018, 'Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods', Foundations of Computational Mathematics, 18, pp. 1199 - 1232, http://dx.doi.org/10.1007/s10208-017-9366-8

Journal articles | 2017

Borwein JM; Li G; Tam MK, 2017, 'Convergence rate analysis for averaged fixed point iterations in common fixed point problems', SIAM Journal on Optimization, 27, pp. 1 - 33, http://dx.doi.org/10.1137/15M1045223

Journal articles | 2017

Che M; Li G; Qi L; Wei Y, 2017, 'Pseudo-spectra theory of tensors and tensor polynomial eigenvalue problems', Linear Algebra and Its Applications, 533, pp. 536 - 572, http://dx.doi.org/10.1016/j.laa.2017.07.026

Journal articles | 2017

Chieu NH; Jeyakumar V; Li G, 2017, 'A convergent hierarchy of SDP relaxations for a class of hard robust global polynomial optimization problems', Operations Research Letters, 45, pp. 325 - 333, http://dx.doi.org/10.1016/j.orl.2017.04.005

Journal articles | 2017

Drusvyatskiy D; Li G; Wolkowicz H, 2017, 'A note on alternating projections for ill-posed semidefinite feasibility problems', Mathematical Programming, 162, pp. 537 - 548, http://dx.doi.org/10.1007/s10107-016-1048-9

Journal articles | 2017

Feng J; Wu D; Gao W; Li G, 2017, 'Uncertainty analysis for structures with hybrid random and interval parameters using mathematical programming approach', Applied Mathematical Modelling, 48, pp. 208 - 232, http://dx.doi.org/10.1016/j.apm.2017.03.066

Journal articles | 2017

Jeyakumar V; Li G, 2017, 'Exact Conic Programming Relaxations for a Class of Convex Polynomial Cone Programs', Journal of Optimization Theory and Applications, 172, pp. 156 - 178, http://dx.doi.org/10.1007/s10957-016-1023-x

Journal articles | 2017

Li G; Liu T; Pong TK, 2017, 'Peaceman–Rachford splitting for a class of nonconvex optimization problems', Computational Optimization and Applications, 68, pp. 407 - 436, http://dx.doi.org/10.1007/s10589-017-9915-8

Journal articles | 2017

Wang Q; Li G; Qi L; Xu Y, 2017, 'New classes of positive semi-definite Hankel tensors', Minimax Theory and its Applications, 2, pp. 231 - 248

Journal articles | 2016

Chen H; Li G; Qi L, 2016, 'Further results on Cauchy tensors and Hankel tensors', Applied Mathematics and Computation, 275, pp. 50 - 62, http://dx.doi.org/10.1016/j.amc.2015.11.051

Journal articles | 2016

Chen H; Li G; Qi L, 2016, 'SOS tensor decomposition: Theory and applications', Communications in Mathematical Sciences, 14, pp. 2073 - 2100, http://dx.doi.org/10.4310/CMS.2016.v14.n8.a1

Journal articles | 2016

Goberna MA; Jeyakumar V; Li G; Linh N, 2016, 'Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints', Operations Research Letters, 44, pp. 67 - 73, http://dx.doi.org/10.1016/j.orl.2015.11.011

Journal articles | 2016

Hu S; Li G; Qi L, 2016, 'A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure', Journal of Optimization Theory and Applications, 168, pp. 446 - 474, http://dx.doi.org/10.1007/s10957-014-0652-1

Journal articles | 2016

Jeyakumar V; Kim S; Lee GM; Li G, 2016, 'Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets', Journal of Global Optimization, 65, pp. 175 - 190, http://dx.doi.org/10.1007/s10898-015-0356-6

Journal articles | 2016

Jeyakumary V; Lasserre JB; Li G; Pham TS, 2016, 'Convergent semidefinite programming relaxations for global bilevel polynomial optimization problems', SIAM Journal on Optimization, 26, pp. 753 - 780, http://dx.doi.org/10.1137/15M1017922

Journal articles | 2016

Li G; Pong TK, 2016, 'Douglas–Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems', Mathematical Programming, 159, pp. 371 - 401, http://dx.doi.org/10.1007/s10107-015-0963-5

Journal articles | 2016

Li G; Qi L; Wang Q, 2016, 'Positive semi-definiteness of generalized anti-circulant tensors', Communications in Mathematical Sciences, 14, pp. 941 - 952, http://dx.doi.org/10.4310/CMS.2016.v14.n4.a3

Journal articles | 2015

Goberna MA; Jeyakumar V; Li G; Vicente-Pérez J, 2015, 'Robust solutions to multi-objective linear programs with uncertain data', European Journal of Operational Research, 242, pp. 730 - 743, http://dx.doi.org/10.1016/j.ejor.2014.10.027

Journal articles | 2015

Jeyakumar V; Lee GM; Li G, 2015, 'Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty', Journal of Optimization Theory and Applications, 164, pp. 407 - 435, http://dx.doi.org/10.1007/s10957-014-0564-0

Journal articles | 2015

Jeyakumar V; Li G; Vicente-Pérez J, 2015, 'Robust SOS-convex polynomial optimization problems: exact SDP relaxations', Optimization Letters, 9, pp. 1 - 18, http://dx.doi.org/10.1007/s11590-014-0732-z

Journal articles | 2015

Jeyakumar V; Li G, 2015, 'A bilevel Farkas lemma to characterizing global solutions of a class of bilevel polynomial programs', Operations Research Letters, 43, pp. 405 - 410, http://dx.doi.org/10.1016/j.orl.2015.05.006

Journal articles | 2015

Jeyakumar V; Li G, 2015, 'A new class of alternative theorems for SOS-convex inequalities and robust optimization', Applicable Analysis, 94, pp. 56 - 74, http://dx.doi.org/10.1080/00036811.2013.859251

Journal articles | 2015

Li G; Mordukhovich BS; Phạm TS, 2015, 'New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors', Mathematical Programming, 153, pp. 333 - 362, http://dx.doi.org/10.1007/s10107-014-0806-9

Journal articles | 2015

Li G; Pong TK, 2015, 'Global convergence of splitting methods for nonconvex composite op timization', SIAM Journal on Optimization, 25, pp. 2434 - 2460, http://dx.doi.org/10.1137/140998135

Journal articles | 2015

Wu D; Gao W; Li G; Tangaramvong S; Tin-Loi F, 2015, 'Robust assessment of collapse resistance of structures under uncertain loads based on Info-Gap model', Computer Methods in Applied Mechanics and Engineering, 285, pp. 208 - 227, http://dx.doi.org/10.1016/j.cma.2014.10.038

Journal articles | 2014

Borwein JM; Li G; Yao L, 2014, 'Analysis of the convergence rate for the cyclic projection algorithm applied to basic semialgebraic convex sets', SIAM Journal on Optimization, 24, pp. 498 - 527, http://dx.doi.org/10.1137/130919052

Journal articles | 2014

Goberna MA; Jeyakumar V; Li G; Vicente-Pérez J, 2014, 'Robust solutions of multiobjective linear semi-infinite programs under constraint data uncertainty', SIAM Journal on Optimization, 24, pp. 1402 - 1419, http://dx.doi.org/10.1137/130939596

Journal articles | 2014

Jeyakumar V; Lasserre JB; Li G, 2014, 'On Polynomial Optimization Over Non-compact Semi-algebraic Sets', Journal of Optimization Theory and Applications, 163, pp. 707 - 718, http://dx.doi.org/10.1007/s10957-014-0545-3

Journal articles | 2014

Jeyakumar V; Li G; Srisatkunarajah S, 2014, 'Global Optimality Principles for Polynomial Optimization over Box or Bivalent Constraints by Separable Polynomial Approximations', Journal of Global Optimization, 58, pp. 31 - 50, http://dx.doi.org/10.1007/s10898-013-0058-x

Journal articles | 2014

Jeyakumar V; Li GY, 2014, 'Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization', Mathematical Programming, 147, pp. 171 - 206, http://dx.doi.org/10.1007/s10107-013-0716-2

Journal articles | 2014

Jeyakumar V; Phaìm TS; Li G, 2014, 'Convergence of the Lasserre hierarchy of SDP relaxations for convex polynomial programs without compactness', Operations Research Letters, 42, pp. 34 - 40, http://dx.doi.org/10.1016/j.orl.2013.11.005

Journal articles | 2014

Li G; Ma AKC; Pong TK, 2014, 'Robust least square semidefinite programming with applications', Computational Optimization and Applications, 58, pp. 347 - 379, http://dx.doi.org/10.1007/s10589-013-9634-8

Journal articles | 2014

Yuan G; Wei Z; Li G, 2014, 'A modified Polak-Ribière-Polyak conjugate gradient algorithm for nonsmooth convex programs', Journal of Computational and Applied Mathematics, 255, pp. 86 - 96, http://dx.doi.org/10.1016/j.cam.2013.04.032

Journal articles | 2013

Bot R; Jeyakumar V; Li G, 2013, 'Robust duality in parametric convex optimization', Set-Valued and Variational Analysis, 21, pp. 177 - 189, http://dx.doi.org/10.1007/s11228-012-0219-y

Journal articles | 2013

Goberna MA; Jeyakumar V; Li G; López MA, 2013, 'Robust linear semi-infinite programming duality under uncertainty', Mathematical Programming, 139, pp. 185 - 203, http://dx.doi.org/10.1007/s10107-013-0668-6

Journal articles | 2013

Hu S; Li G; Qi L; Song Y, 2013, 'Finding the Maximum Eigenvalue of Essentially Nonnegative Symmetric Tensors via Sum of Squares Programming', Journal of Optimization and its application, 158, pp. 717 - 738, http://dx.doi.org/10.1007/s10957-013-0293-9

Journal articles | 2013

Jeyakumar V; Li G; Mordukhovich B; Wang J, 2013, 'Robust best approximation with interpolation constraints under ellipsoidal uncertainty: Strong duality and nonsmooth Newton methods', Nonlinear Analysis - Theory Methods and Applications, 81, pp. 1 - 11, http://dx.doi.org/10.1016/j.na.2012.12.009

Journal articles | 2013

Jeyakumar V; Li G; Srisatkunarajah S, 2013, 'Strong duality for robust minimax fractional programming problems', European Journal of Operational Research, 228, pp. 331 - 336, http://dx.doi.org/10.1016/j.ejor.2013.02.015

Journal articles | 2013

Jeyakumar V; Li G; Wang J, 2013, 'Some robust convex programs without duality gap', Journal of Convex Analysis, 20, pp. 377 - 394, http://web.maths.unsw.edu.au/~gyli/papers/jlw_duality_gap.pdf

Journal articles | 2013

Jeyakumar V; Li G, 2013, 'Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty', Journal of Global Optimization, 55, pp. 209 - 226, http://dx.doi.org/10.1007/s10898-012-9857-8

Journal articles | 2013

Li G; Qi L; Yu G, 2013, 'Semismoothness of the Maximum Eigenvalue Function of a Symmetric Tensor and its Application', Linear Algebra and its Applications, 438, pp. 813 - 833, http://dx.doi.org/10.1016/j.laa.2011.10.043

Journal articles | 2013

Li G; Qi L; Yu G, 2013, 'The Z-eigenvalues of a Symmetric Tensor and its Application to Spectral Hypergraph Theory', Numerical Linear Algebra with Applications, 20, pp. 1001 - 1029, http://dx.doi.org/10.1002/nla.1877

Journal articles | 2013

Li G, 2013, 'Global error bounds for piecewise convex polynomials', Mathematical Programming, Series A, 137, pp. 37 - 64, http://dx.doi.org/10.1007/s10107-011-0481-z

Journal articles | 2012

Jeyakumar V; Li G; Lee GM, 2012, 'Robust duality for generalized convex programming prolems under data uncertainty', Nonlinear Analysis - Theory Methods and Applications, 75, pp. 1362 - 1373, http://dx.doi.org/10.1016/j.na.2011.04.006

Journal articles | 2012

Jeyakumar V; Li G; Suthaharan S, 2012, 'Support vector machine classifiers with uncertain knowledge sets via robust optimization', Optimization, 63, pp. 1099 - 1116, http://dx.doi.org/10.1080/02331934.2012.703667

Journal articles | 2012

Jeyakumar V; Li G, 2012, 'Exact SDP relaxations for classes of nonlinear semidefinite programming problems', Operations Research Letters, 40, pp. 529 - 536, http://dx.doi.org/10.1016/j.orl.2012.09.006

Journal articles | 2012

Jeyakumar V; Li G, 2012, 'Strong duality in robust semi-definite linear programming under data uncertainty', Optimization, 63, pp. 713 - 733, http://dx.doi.org/10.1080/02331934.2012.690760

Journal articles | 2012

Jeyakumar V; Wang J; Li G, 2012, 'Lagrange multiplier characterizations of robust best approximations under constraint data uncertainty', Journal of Mathematical Analysis and Applications, 393, pp. 285 - 297, http://dx.doi.org/10.1016/j.jmaa.2012.03.037

Journal articles | 2012

Li G; Mordukhovich B, 2012, 'Hölder Metric Subregularity with Applications to Proximal Point Method', SIAM Journal on Optimization, 22, pp. 1655 - 1684, http://dx.doi.org/10.1137/120864660

Journal articles | 2012

Li G, 2012, 'Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition', Journal of Optimization Theory and Applications, 152, pp. 710 - 726, http://dx.doi.org/10.1007/s10957-011-9930-3

Journal articles | 2011

Huang L; Li G; Yuan G, 2011, 'A Look at the Tool of BYRD and NOCEDAL', American Journal of Computational Mathematics, 01, pp. 240 - 246, http://dx.doi.org/10.4236/ajcm.2011.14028

Journal articles | 2011

Jeyakumar V; Li G; Lee GM, 2011, 'A robust Von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty', Operations Research Letters, 39, pp. 109 - 114, http://dx.doi.org/10.1016/j.orl.2011.02.007

Journal articles | 2011

Jeyakumar V; Li G, 2011, 'Necessary global optimality conditions for nonlinear programming problems with polynomial constraints', Mathematical Programming, 126, pp. 393 - 399, http://dx.doi.org/10.1007/s10107-009-0283-8

Journal articles | 2011

Jeyakumar V; Li G, 2011, 'Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems', Journal of Global Optimization, 49, pp. 1 - 14, http://dx.doi.org/10.1007/s10898-009-9518-8

Journal articles | 2011

Jeyakumar V; Li G, 2011, 'Robust Farkas’ lemma for uncertain linear systems with applications', Positivity, 15, pp. 331 - 342, http://dx.doi.org/10.1007/s11117-010-0078-4

Journal articles | 2011

Jeyakumar V; Li G, 2011, 'Robust duality for fractional programming problems with constraint-wise data uncertainty', Journal of Optimization Theory and Applications, 151, pp. 292 - 303, http://dx.doi.org/10.1007/s10957-011-9896-1

Journal articles | 2011

Li G; Jeyakumar V; Lee G, 2011, 'Robust conjugate duality for convex optimization under uncertainty with application to data classification', Nonlinear Analysis - Theory Methods and Applications, 74, pp. 2327 - 2341, http://dx.doi.org/10.1016/j.na.2010.11.036

Journal articles | 2011

Li G, 2011, 'A note on nonconvex minimax theorem with separable homogeneous polynomials', Journal of Optimization Theory and Applications, 150, pp. 194 - 203, http://dx.doi.org/10.1007/s10957-011-9827-1

Journal articles | 2011

Tang CM; Jian JB; Li GY, 2011, 'A working set SQCQP algorithm with simple nonmonotone penalty parameters', Journal of Computational and Applied Mathematics, 236, pp. 1382 - 1398, http://dx.doi.org/10.1016/j.cam.2011.09.002

Journal articles | 2010

Jeyakumar V; Li G, 2010, 'Characterizing robust set containments and solutions of uncertain linear programs without qualifications', Operations Research Letters, 38, pp. 188 - 194, http://dx.doi.org/10.1016/j.orl.2009.12.004

Journal articles | 2010

Jeyakumar V; Li G, 2010, 'New strong duality results for convex programs with separable constraints', European Journal of Operational Research, 207, pp. 1203 - 1209, http://dx.doi.org/10.1016/j.ejor.2010.07.007

Journal articles | 2010

Jeyakumar V; Li G, 2010, 'Strong duality in robust convex programming: complete characterizations', SIAM Journal on Optimization, 20, pp. 3384 - 3407, http://dx.doi.org/10.1137/100791841

Journal articles | 2010

Li G; Tang C; Wei Z, 2010, 'Error bound results for generalized D-gap functions of nonsmooth variational inequality problems', Journal of Computational and Applied Mathematics, 233, pp. 2795 - 2806, http://dx.doi.org/10.1016/j.cam.2009.11.025

Journal articles | 2010

Li G, 2010, 'On the asymptotically well behaved functions and global error bound for convex polynomials', SIAM Journal on Optimization, 20, pp. 1923 - 1943, http://dx.doi.org/10.1137/080733668

Journal articles | 2009

Jeyakumar V; Lee GM; Li G, 2009, 'Alternative theorems for quadratic inequality systems and global quadratic optimization', SIAM Journal on Optimization, 20, pp. 983 - 1001, http://dx.doi.org/10.1137/080736090

Journal articles | 2009

Jeyakumar V; Li G; Huy N, 2009, 'Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization', Optimization and Engineering, 10, pp. 491 - 503, http://dx.doi.org/10.1007/s11081-008-9076-9

Journal articles | 2009

Jeyakumar V; Li G, 2009, 'Farkas' lemma for separable sublinear inequalities without qualifications', Optimization Letters, 3, pp. 537 - 545, http://dx.doi.org/10.1007/s11590-009-0133-x

Journal articles | 2009

Jeyakumar V; Li G, 2009, 'New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs', Nonlinear Analysis - Theory Methods and Applications, 71, pp. e2239 - e2249, http://dx.doi.org/10.1016/j.na.2009.05.009

Journal articles | 2009

Jeyakumar V; Li G, 2009, 'Qualification-free optimality conditions for convex programs with separable inequality constraints', Journal of Convex Analysis, 16, pp. 845 - 856

Journal articles | 2009

Jeyakumar V; Li G, 2009, 'Stable zero duality gaps in convex programming: Complete dual characterisations with applications to semidefinite programs', Journal of Mathematical Analysis and Applications, 360, pp. 156 - 167, http://dx.doi.org/10.1016/j.jmaa.2009.06.043

Journal articles | 2009

Li G; Ng KF, 2009, 'Error bounds of generalized D-gap functions for nonsmooth and nonmonotone variational inequality problems', SIAM Journal on Optimization, 20, pp. 667 - 690, http://dx.doi.org/10.1137/070696283

Journal articles | 2008

Li G; Ng KF, 2008, 'On Extension of Fenchel Duality and its Application', SIAM Journal on Optimization, 19, pp. 1489 - 1509, http://dx.doi.org/10.1137/080716803

Journal articles | 2008

Li G; Tang C; Yu G; Wei Z, 2008, 'On a Separation Principle for Nonconvex Sets', Set - Valued Analysis, 16, pp. 851 - 860, http://dx.doi.org/10.1007/s11228-008-0099-3

Journal articles | 2008

Wei ZX; Li G; Qi LQ, 2008, 'Global convergence of the Polak-Ribiere- Polyak conjugate gradient method with inexact line searches for nonconvex unconstrained optimization problems, Mathematics of Computation', Mathematics of Computation, 77, pp. 2173 - 2193, http://dx.doi.org/10.1090/S0025-5718-08-02031-0

Journal articles | 2008

Yu G; Guan L; Li G, 2008, 'Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property', Journal of Industrial and Management Optimization, 4, pp. 565 - 579, http://dx.doi.org/10.3934/jimo.2008.4.565

Journal articles | 2007

Li G; Ng KF; Zheng XY, 2007, 'Unified approach to some geometric results in variational analysis', Journal of Functional Analysis, 248, pp. 317 - 343, http://dx.doi.org/10.1016/j.jfa.2007.04.001

Journal articles | 2007

Li G; Tang C; Wei ZX, 2007, 'New conjugacy condition and related new conjugate gradient methods for unconstrained optimization', Journal of Computational and Applied Mathematics, 202, pp. 523 - 539, http://dx.doi.org/10.1016/j.cam.2006.03.005

Journal articles | 2007

Wei ZX; Tang C; Li G, 2007, 'A new version of the Liu-Storey conjugate gradient method', Applied Mathematics and Computation, 189, pp. 302 - 313, http://dx.doi.org/10.1016/j.amc.2006.11.098

Journal articles | 2006

Wei ZX; Li G; Qi LQ, 2006, 'New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems', Applied Mathematics and Computation, 179, pp. 407 - 430, http://dx.doi.org/10.1016/j.amc.2005.11.150

Journal articles | 2006

Wei ZX; Li G; Qi LQ, 2006, 'New quasi-Newton methods for unconstrained optimization problems', Applied Mathematics and Computation, 175, pp. 1156 - 1188, http://dx.doi.org/10.1016/j.amc.2005.08.027
Preprints | 2022

Pham TN; Dao MN; Shah R; Sultanova N; Li G; Islam S, 2022, A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems, , http://dx.doi.org/10.48550/arxiv.2208.12432

Preprints | 2021

Zeng L; Zhang Y; Li G; Pong TK, 2021, Frank-Wolfe-type methods for a class of nonconvex inequality-constrained problems, , http://dx.doi.org/10.48550/arxiv.2112.14404

Preprints | 2021

Zhang Y; Li G; Pong TK; Xu S, 2021, Retraction-based first-order feasible methods for difference-of-convex programs with smooth inequality and simple geometric constraints, , http://dx.doi.org/10.48550/arxiv.2106.08584

Preprints | 2020

Boţ RI; Dao MN; Li G, 2020, Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs, , http://dx.doi.org/10.48550/arxiv.2003.04124

Preprints | 2020

Boţ RI; Dao MN; Li G, 2020, Inertial Proximal Block Coordinate Method for a Class of Nonsmooth Sum-of-Ratios Optimization Problems, , http://dx.doi.org/10.48550/arxiv.2011.09782

Preprints | 2020

Goberna MA; Jeyakumar V; Li G, 2020, Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semidefinite Programs, , http://dx.doi.org/10.48550/arxiv.2007.07599

Preprints | 2020

Woolnough D; Jeyakumar V; Li G, 2020, Exact Conic Programming Reformulations of Two-Stage Adjustable Robust Linear Programs with New Quadratic Decision Rules, , http://dx.doi.org/10.48550/arxiv.2002.05223

Preprints | 2019

Yu P; Li G; Pong TK, 2019, Kurdyka-Łojasiewicz exponent via inf-projection, , http://dx.doi.org/10.48550/arxiv.1902.03635

Preprints | 2018

Bello-Cruz Y; Li G; Nghia TTA, 2018, On the Q-linear convergence of forward-backward splitting method and uniqueness of optimal solution to Lasso, , http://dx.doi.org/10.48550/arxiv.1806.06333

Preprints | 2017

Bomze IM; Jeyakumar V; Li G, 2017, Extended Trust-Region Problems with One or Two Balls: Exact Copositive and Lagrangian Relaxations, , http://dx.doi.org/10.48550/arxiv.1702.08113

Preprints | 2017

Chuong TD; Jeyakumar V; Li G, 2017, A Bounded Degree Lasserre Hierarchy with SOCP Relaxations for Global Polynomial Optimization and Applications, , http://dx.doi.org/10.48550/arxiv.1710.06598

Conference Papers | 2017

Feng J; Wu D; Gao W; Li G, 2017, 'Hybrid random and fuzzy analysis of structural response using mathematical programming approach', in 9th Australasian Congress on Applied Mechanics, ACAM 2017

Conference Papers | 2017

Feng J; Wu D; Gao W; Li G, 2017, 'Non-deterministic free vibration analysis of structures with random and fuzzy parameters', in ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE), Tampa, Florida, USA, presented at ASME 2017 International Mechanical Engineering Congress and Exposition, Tampa, Florida, USA, 03 November 2017 - 09 November 2017, http://dx.doi.org/10.1115/IMECE2017-71059

Conference Papers | 2016

Gao W; Feng J; Wu D; Li G, 2016, 'Unified stochastic and non-stochastic free vibration analysis of structure', in Hao H; Zhang C (ed.), Mechanics of Structures and Materials: Advancements and Challenges, CRC PRESS / BALKEMA, Perth, Australia, pp. 1809 - 1814, presented at The 24th Australasian Conference on the Mechanics of Structures and Materials, Perth, Australia, 06 December 2016 - 09 December 2016

Preprints | 2016

Li G; Pong TK, 2016, Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods, , http://dx.doi.org/10.48550/arxiv.1602.02915

Preprints | 2015

Borwein JM; Li G; Tam MK, 2015, Convergence rate analysis for averaged fixed point iterations in the presence of Hölder regularity, , http://dx.doi.org/10.48550/arxiv.1510.06823

Preprints | 2015

Li G; Liu T; Pong TK, 2015, Peaceman-Rachford splitting for a class of nonconvex optimization problems, , http://dx.doi.org/10.48550/arxiv.1507.00887

Preprints | 2015

Li G; Mordukhovich BS; Nghia TTA; Pham TS, 2015, Error Bounds for Parametric Polynomial Systems with Applications to Higher-Order Stability Analysis and Convergence Rates, , http://dx.doi.org/10.48550/arxiv.1509.03742

Preprints | 2014

Li G; Pong TK, 2014, Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems, , http://dx.doi.org/10.48550/arxiv.1409.8444

Preprints | 2014

Li G; Pong TK, 2014, Global convergence of splitting methods for nonconvex composite optimization, , http://dx.doi.org/10.48550/arxiv.1407.0753

Preprints | 2013

Borwein JM; Li G; Yao L, 2013, Analysis of the convergence rate for the cyclic projection algorithm applied to basic semi-algebraic convex sets, , http://dx.doi.org/10.48550/arxiv.1304.7965

Australian Research Council Discovery Grant (2021-2023), V. Jeyakumar, G. Li, J.B. Lasserre, M. Goberna and I. M. Bomze, Data-Driven Multistage Robust Optimization-the New Frontier in Optimization.
Australian Research Council Discovery Grant (DP190100555), 2019-2021, G. Li, B. Mordukhovich, R. Bot, Innovations in sparse optimisation: big data nonsmooth optimisation.
Australian Research Council Discovery Grant (DP180100745), 2018-2020, V. Jeyakumar, G. Li, J.B. Lasserre, L.Q. Qi and D. Henrion: New Mathematics for Multiextremal Semialgebraic Optimization and Diffusion Tensor Imaging.
Australian Research Council Future Fellowship (FT130100038), 2014-2018, G. Li, A new optimization approach for tensor extreme eigenvalue problems: modern techniques for multi-relational data analysis.
ARC Research Hub Project, 2017-2021, W. Gao, Y.X. Zhang and G. Li, Performance assessment and optimal design for nano and composite structures, under ARC Linkage Scheme and administered through the ARC Research Hub for Nanoscience-based construction material manufacturing (IH150100006).
UNSW Science Gold Star Grant, 2017, V. Jeyakumar, G. Li, C. Thai Doan: Numerically Certifiable Mathematics for Multi-Extremal Global Optimization.
Australian Research Council Discovery Grant (DP120100467), 2012-2014, V. Jeyakumar, G. Li and M. A, Goberna: New Theory and Methods for Robust Global Optimization: Modern Decision-Making under Uncertain Conditions.
Australian Research Council Discovery Grant (DP1092508), 2010-2013, V. Jeyakumar, G. Li, G. M. Lee, B.S. Mordukhovich and S. Kim, A new improved solution to global optimization over multivariate polynomials: Mathematical principles, numerical methods and selected applications.

[02/2023] Fellow of Australian Mathematical Society
[12/2022] The 2022 Australian Mathematical Society Medal.
[2019 & 2020] Cited as the field leader in Mathematical Optimisation by the RESEARCH report in The Australian, which profiles the Top 250 researchers in Australia.
[11/2019]: Joint winner of the 2019 Journal of Global Optimization Best Paper Award, https://sites.google.com/site/jogobestpaper/
[11/2019]: 2019 International Consortium of Chinese Mathematicians (ICCM) Best Paper Award.
[10/2017] Outstanding Reviewer Award for the journal ``European Journal of Operation Research''.
[01/2017] Optimization Letters (OPTL) Best Paper Award for 2015.
[01/2014-01/2018] Future Fellowship from Australian Research Council: Future fellowship is a four-year fellowship from Australian Research Council for outstanding mid-career researchers (5-15 years post-PhD)
[01/2017] UNSW Science Gold Star Award for the project ``Numerically Certifiable Mathematics for Multi-Extremal Global Optimization''.
[08/2013] Invited visiting fellowship from Isaac Newton Institute for Mathematical Sciences, University of Cambridge, United Kingdom.
[2011 & 2012] International Collaboration Award from Australian Research Council.
[01/2010-12/2013] Australian Postdoctoral Fellowship from Australian Research Council.

Professional Activities

[Since 01/2023] Associate Editor of the journal "SIAM Journal on Optimization".
[Since 01/2020] Associate Editor of the Springer journal "Optimization Letters".
[Since 01/2016] Associate Editor of the Springer journal ``Journal of Optimization Theory and its Applications".
[Since 01/2015] Associate Editor of the Springer journal ``Mathematical Methods of Operations Research".
[07/2020 - 07/2021] Guest editor for the Topical Collection “Mathematics of Computation and Optimisation” (MoCaO) in the Springer Journal "Advances in Computational Mathematics".

Recent Invited Plenary Presentations

Special Invited Lecture for RAMP Symposium on Mathematical Optimisation , Research Association of Mathematical Programming (RAMP) of the Operations Research Society of Japan, Oct. 7, 2022, online
One World Optimization Seminar (OWS): available on youtube, Dec. 7, 2020, online.
2019 The Internatinoal Consortium of Chinese Mathematicians (ICCM), Best Paper Award Lecture, Dec. 16-18, Sanya, China.
The AMSI Optimise event (June 26-30, 2017) as a national plenary speaker: a five-day symposium inspiring industry and research collaboration, organized by Australian Mathematical Science Institute: 1 hour's presentation.
The international conference “Mathematical Optimisation Down Under (MODU2016)" as a plenary speaker (organized by Australian Mathematical Science Institute), 18-22 July 2016, Melbourne, Australia: 1 hour's presentation.
International Conference in Optimization Theory and its Applications (ALEL 2016) as an invited plenary speaker, 6-8, June 2016, Cartagena, Spain: 1 hour's presentation.
The 2014 International Conference on Tensors and Matrices and their application as an invited plenary speaker,, Suzhou, P.R. China, Dec. 17-20, 2014: 1 hour's presentation.

I was the director of the AMSI Summer School 2019 at University of New South Wales.

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