Associate Professor Robert Womersley
Honorary Associate Professor

Associate Professor Robert Womersley

Science
School of Mathematics & Statistics

My research interested are in the development and application of computational methods for optimization problems, computational mathematics in general, but especially applied to problems of approximation and numerical integration on the sphere, high performance computing and problems in computational finance, such as calibration of financial models to market data.
Phone
9385 7043
E-mail
R.Womersley@unsw.edu.au
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 3062
  • Books | 1997
    1997, Computational nonsmooth optimization, Qi L; Ruszczynski A; Womersley RS, (eds.), Mathematical Programming Society, North Holland
    Books | 1995
    Du D-Z; Qi L; Womersley RS, 1995, Recent Advances in Nonsmooth Optimization, WORLD SCIENTIFIC, http://dx.doi.org/10.1142/2752
  • Book Chapters | 2018
    Brauchart JS; Dragnev PD; Saff EB; Womersley RS, 2018, 'Logarithmic and riesz equilibrium for multiple sources on the sphere: The exceptional case', in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 179 - 203, http://dx.doi.org/10.1007/978-3-319-72456-0_10
    Book Chapters | 2015
    Hesse K; Sloan IH; Womersley RS, 2015, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1 - 35, http://dx.doi.org/10.1007/978-3-642-27793-1_40-3
    Book Chapters | 2015
    Hesse K; Sloan IH; Womersley RS, 2015, 'Numerical integration on the sphere', in Handbook of Geomathematics: Second Edition, pp. 2671 - 2710, http://dx.doi.org/10.1007/978-3-642-54551-1_40
    Book Chapters | 2013
    Hesse K; Sloan IH; Womersley RS, 2013, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1 - 35, http://dx.doi.org/10.1007/978-3-642-27793-1_40-2
    Book Chapters | 2010
    Hesse K; Sloan IH; Womersley RS, 2010, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1185 - 1219, http://dx.doi.org/10.1007/978-3-642-01546-5_40
    Book Chapters | 2010
    Hesse K; Sloan IH; Womersley RS, 2010, 'Numerical Integration on the Sphere', in Freeden W; Nashed MZ; Sonar T (ed.), Handbook of Geomathematics, edn. 1st, Springer, Berlin, pp. 1187 - 1220
  • Journal articles | 2022
    Chafaï D; Saff EB; Womersley RS, 2022, 'On the solution of a Riesz equilibrium problem and integral identities for special functions', Journal of Mathematical Analysis and Applications, pp. 126367 - 126367, http://dx.doi.org/10.1016/j.jmaa.2022.126367
    Journal articles | 2021
    Hamann J; Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2021, 'A new probe of Gaussianity and isotropy with application to cosmic microwave background maps', International Journal of Modern Physics C, vol. 32, http://dx.doi.org/10.1142/S0129183121500844
    Journal articles | 2021
    Hesse K; Sloan IH; Womersley RS, 2021, 'Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data', Journal of Computational and Applied Mathematics, vol. 382, pp. 113061 - 113061, http://dx.doi.org/10.1016/j.cam.2020.113061
    Journal articles | 2021
    Sourisseau M; Wang YG; Womersley RS; Wu HT; Yu WH, 2021, 'Improve concentration of frequency and time (ConceFT) by novel complex spherical designs', Applied and Computational Harmonic Analysis, vol. 54, pp. 137 - 144, http://dx.doi.org/10.1016/j.acha.2021.02.003
    Journal articles | 2019
    Gia QTL; Sloan IH; Womersley RS; Wang YG, 2019, 'Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere', Applied and Computational Harmonic Analysis, http://dx.doi.org/10.1016/j.acha.2019.01.005
    Journal articles | 2019
    Wang YG; Womersley RS; Wu H-T; Yu W-H, 2019, 'Numerical computation of triangular complex spherical designs with small mesh ratio', , http://arxiv.org/abs/1907.13493v3
    Journal articles | 2018
    Chen X; Womersley RS, 2018, 'Spherical designs and nonconvex minimization for recovery of sparse signals on the sphere', SIAM Journal on Imaging Sciences, vol. 11, pp. 1390 - 1415, http://dx.doi.org/10.1137/17M1147378
    Journal articles | 2018
    Womersley RS, 2018, 'Efficient spherical designs with good geometric properties', Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 1243 - 1285, http://dx.doi.org/10.1007/978-3-319-72456-0_57
    Journal articles | 2017
    Hesse K; Sloan IH; Womersley RS, 2017, 'Radial basis function approximation of noisy scattered data on the sphere', Numerische Mathematik, vol. 137, pp. 579 - 605, http://dx.doi.org/10.1007/s00211-017-0886-6
    Journal articles | 2017
    Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2017, 'Needlet approximation for isotropic random fields on the sphere', Journal of Approximation Theory, vol. 216, pp. 86 - 116, http://dx.doi.org/10.1016/j.jat.2017.01.001
    Journal articles | 2017
    Wang YG; Le Gia QT; Sloan IH; Womersley RS, 2017, 'Fully discrete needlet approximation on the sphere', Applied and Computational Harmonic Analysis, vol. 43, pp. 292 - 316, http://dx.doi.org/10.1016/j.acha.2016.01.003
    Journal articles | 2016
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2016, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, vol. 27, pp. 1 - 20, http://dx.doi.org/10.1080/10586458.2016.1226209
    Journal articles | 2016
    Wang YG; Sloan IH; Womersley RS, 2016, 'Riemann Localisation on the Sphere', Journal of Fourier Analysis and Applications, vol. 24, pp. 1 - 43, http://dx.doi.org/10.1007/s00041-016-9496-4
    Journal articles | 2015
    Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2015, 'Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces', Journal of Mathematical Analysis and Applications, vol. 431, pp. 782 - 811, http://dx.doi.org/10.1016/j.jmaa.2015.05.079
    Journal articles | 2014
    An C; Chen X; Sloan IH; Womersley RS, 2014, 'Erratum: Regularized least squares approximations on the sphere using spherical designs (SIAM Journal on Numerical Analysis (2012) 50 (1513-1534))', SIAM Journal on Numerical Analysis, vol. 52, pp. 2205 - 2206, http://dx.doi.org/10.1137/140962504
    Journal articles | 2014
    Brauchart JS; Saff EB; Sloan IH; Womersley RS, 2014, 'QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere', Mathematics of Computation, vol. 83, pp. 2821 - 2851, http://dx.doi.org/10.1090/S0025-5718-2014-02839-1
    Journal articles | 2014
    Chernih A; Sloan IH; Womersley RS, 2014, 'Wendland functions with increasing smoothness converge to a Gaussian', Advances in Computational Mathematics, vol. 40, pp. 185 - 200, http://dx.doi.org/10.1007/s10444-013-9304-5
    Journal articles | 2012
    An C; Chen X; Sloan IH; Womersley RS, 2012, 'Regularized least squares approximations on the sphere using spherical designs', SIAM Journal on Numerical Analysis, vol. 50, pp. 1513 - 1534, http://dx.doi.org/10.1137/110838601
    Journal articles | 2012
    Hesse K; Womersley RS, 2012, 'Numerical integration with polynomial exactness over a spherical cap', Advances in Computational Mathematics, vol. 36, pp. 451 - 483, http://dx.doi.org/10.1007/s10444-011-9187-2
    Journal articles | 2012
    Sloan IH; Womersley RS, 2012, 'Filtered hyperinterpolation: a constructive polynomial approximation on the sphere', International Journal on Geomathematics, vol. 3, pp. 95 - 117, http://dx.doi.org/10.1007/s13137-011-0029-7
    Journal articles | 2011
    Chen X; Womersley RS; Ye JJ, 2011, 'Minimizing the condition number of a gram matrix', SIAM Journal on Optimization, vol. 21, pp. 127 - 148, http://dx.doi.org/10.1137/100786022
    Journal articles | 2010
    An C; Chen X; Sloan IH; Womersley RS, 2010, 'Well conditioned spherical designs for integration and interpolation on the two-sphere', SIAM Journal on Numerical Analysis, vol. 48, pp. 2135 - 2157, http://dx.doi.org/10.1137/100795140
    Journal articles | 2009
    Sloan IH; Womersley RS, 2009, 'A variational characterisation of spherical designs', Journal of Approximation Theory, vol. 159, pp. 308 - 318, http://dx.doi.org/10.1016/j.jat.2009.02.014
    Journal articles | 2008
    Evans JR; Womersley RS; Wong D; Woodbury G, 2008, 'Operational Risk in Banks', JASSA - Journal of the Securities Institute of Australia, vol. 2, pp. 9 - 16
    Journal articles | 2008
    Kuo FY; Dunsmuir WT; Sloan IH; Wand MP; Womersley RS, 2008, 'Quasi-Monte Carlo for highly structured generalised response models', Methodology and Computing in Applied Probability, vol. 10, pp. 239 - 275, http://dx.doi.org/10.1007/s11009-007-9045-3
    Journal articles | 2008
    Leopardi PC; Womersley RS, 2008, 'Porting a sphere optimization program from LAPACK to ScaLAPACK', The ANZIAM Journal, vol. 50, pp. C204 - C219
    Journal articles | 2008
    Polak E; Womersley RS; Yin H, 2008, 'An algorithm based on active sets and smoothing for discretized semi-infinile minimax problems', Journal of Optimization Theory and Applications, vol. 138, pp. 311 - 328, http://dx.doi.org/10.1007/s10957-008-9355-9
    Journal articles | 2006
    Chen X; Womersley RS, 2006, 'Existence of solutions to systems of underdetermined equations and spherical designs', SIAM Journal on Numerical Analysis, vol. 44, pp. 2326 - 2341, http://dx.doi.org/10.1137/050626636
    Journal articles | 2006
    Jeyakumar V; Ormerod JT; Womersley RS, 2006, 'Knowledge-based semidefinite linear programming classifiers', Optimization Methods and Software, vol. 21, pp. 693 - 706, http://dx.doi.org/10.1080/10556780500137066
    Journal articles | 2004
    Sloan IH; Womersley RS, 2004, 'Extremal systems of points and numerical integration on the sphere', Advances in Computational Mathematics, vol. 21, pp. 107 - 125
    Journal articles | 2003
    Polak E; Royset JO; Womersley RS, 2003, 'Algorithms with adaptive smoothing for finite minimax problems', Journal of Optimization Theory and Applications, vol. 119, pp. 459 - 484, http://dx.doi.org/10.1023/B:JOTA.0000006685.60019.3e
    Journal articles | 2002
    Sloan IH; Womersley RS, 2002, 'Good approximation on the sphere, with application to geodesy and the scattering of sound', Journal of Computational and Applied Mathematics, vol. 149, pp. 227 - 237, http://dx.doi.org/10.1016/S0377-0427(02)00532-0
    Journal articles | 2002
    Sun D; Womersley RS; Qi H, 2002, 'A feasible semismooth asymptotically Newton method for mixed complementarity problems', Mathematical Programming, vol. 94, pp. 167 - 187, http://dx.doi.org/10.1007/s10107-002-0305-2
    Journal articles | 2001
    Gonsalkorale K; Womersley RS, 2001, 'Multistage quadratic stochastic programming', Journal of Computational and Applied Mathematics, vol. 129, pp. 105 - 138, http://dx.doi.org/10.1016/S0377-0427(00)00545-8
    Journal articles | 2001
    Womersley RS; Sloan IH, 2001, 'How good can polynomial interpolation on the sphere be?', Advances in Computational Mathematics, vol. 14, pp. 195 - 226, http://dx.doi.org/10.1023/A:1016630227163
    Journal articles | 2000
    Chen X; Womersley RS, 2000, 'Random test problems and parallel methods for quadratic programs and quadratic stochastic programs', Optimization Methods and Software, vol. 13, pp. 275 - 306, http://dx.doi.org/10.1080/10556780008805789
    Journal articles | 2000
    Sloan IH; Womersley RS, 2000, 'Constructive polynomial approximation on the sphere', Journal of Approximation Theory, vol. 103, pp. 91 - 118, http://dx.doi.org/10.1006/jath.1999.3426
    Journal articles | 2000
    Womersley RS, 2000, 'A continuous minimax problem for calculating minimum norm polynomial interpolation points on the sphere ANZIAM journal', Journal of Australian Mathematical Society B, pp. 1536 - 1557
    Journal articles | 1999
    Sun D; Womersley RS, 1999, 'A new unconstrained differentiable merit function for box constrained variational inequality problems and a damped Gauss-Newton method', SIAM Journal on Optimization, vol. 9, pp. 388 - 413, http://dx.doi.org/10.1137/S1052623496314173
    Journal articles | 1998
    Chen X; Womersley RS, 1998, 'Stochastic programming', New South Wales Centre for Parallel Computine, pp. 10 - 10
    Journal articles | 1998
    Khoury F; Standish RK; Womersley RS, 1998, 'Parallel triangular system solvers', New South Wales Centre for Parallel Computine, pp. 21 - 22
    Journal articles | 1996
    Qi L; Womersley RS, 1996, 'On extreme singular values of matrix valued functions', Journal of Convex Analysis, vol. 3, pp. 153 - 166
    Journal articles | 1996
    Tin Loi FS; Qi L; Wei Z; Womersley RS, 1996, 'Stochastic ultimate load analysis: models and solution methods', Numerical Functional Analysis and Optimization, vol. 17, pp. 1029 - 1043, http://dx.doi.org/10.1080/01630569608816740
    Journal articles | 1995
    Chen X; Qi L; Womersley RS, 1995, 'Newton's method for quadratic stochastic programs with recourse', Journal of Computational and Applied Mathematics, vol. 60, pp. 29 - 46, http://dx.doi.org/10.1016/0377-0427(94)00082-C
    Journal articles | 1995
    Overton ML; Womersley RS, 1995, 'Second derivatives for optimizing eigenvalues of symmetric matrices', SIAM Journal on Matrix Analysis and Applications, vol. 16, pp. 697 - 718
    Journal articles | 1995
    Qi L; Womersley RS, 1995, 'An SQP algorithm for extended linear-quadratic problems in stochastic programming', Annals of Operations Research, vol. 56, pp. 251 - 285, http://dx.doi.org/10.1007/BF02031711
    Journal articles | 1993
    Overton ML; Womersley RS, 1993, 'Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices', Mathematical Programming, vol. 62, pp. 321 - 357, http://dx.doi.org/10.1007/BF01585173
    Journal articles | 1992
    Overton ML; Womersley RS, 1992, 'On the Sum of the Largest Eigenvalues of a Symmetric Matrix', SIAM Journal on Matrix Analysis and Applications, vol. 13, pp. 41 - 45, http://dx.doi.org/10.1137/0613006
    Journal articles | 1990
    Osborne MR; Womersley RS, 1990, 'Strong uniqueness in sequential linear programming', The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, vol. 31, pp. 379 - 384, http://dx.doi.org/10.1017/s0334270000006731
    Journal articles | 1988
    Overton ML; Womersley RS, 1988, 'On Minimizing the Special Radius of a Nonsymmetric Matrix Function: Optimality Conditions and Duality Theory', SIAM Journal on Matrix Analysis and Applications, vol. 9, pp. 473 - 498, http://dx.doi.org/10.1137/0609040
    Journal articles | 1986
    Osborne MR; Pruess SA; Womersley RS, 1986, 'Concise representation of generalised gradients', The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, vol. 28, pp. 57 - 74, http://dx.doi.org/10.1017/s0334270000005191
    Journal articles | 1986
    Womersley RS, 1986, 'Censored Discrete Linear $l_1 $ Approximation', SIAM Journal on Scientific and Statistical Computing, vol. 7, pp. 105 - 122, http://dx.doi.org/10.1137/0907008
    Journal articles | 1986
    Womersley RS; Fletcher R, 1986, 'An algorithm for composite nonsmooth optimization problems', Journal of Optimization Theory and Applications, vol. 48, pp. 493 - 523, http://dx.doi.org/10.1007/BF00940574
    Journal articles | 1985
    Womersley RS, 1985, 'Local properties of algorithms for minimizing nonsmooth composite functions', Mathematical Programming, vol. 32, pp. 69 - 89, http://dx.doi.org/10.1007/BF01585659
    Journal articles | 1983
    Teo KL, 1983, 'A Control Parametrization Algorithm for Optimal Control Problems Involving Linear Systems and Linear Terminal Inequality Constraints', Numerical Functional Analysis and Optimization, vol. 6, pp. 291 - 313, http://dx.doi.org/10.1080/01630568308816168
    Journal articles |
    Sourisseau M; Wang YG; Womersley RS; Wu H-T; Yu W-H, 'Improve Concentration of Frequency and Time (Conceft) by Novel Complex Spherical Designs', , http://dx.doi.org/10.1101/2020.11.23.394007
  • Working Papers | 2019
    Hamann J; Gia QTL; Sloan IH; Wang YG; Womersley RS, 2019, A New Probe of Gaussianity and Isotropy applied to the CMB Maps, http://dx.doi.org, http://arxiv.org/abs/1911.11442v2
    Working Papers | 2018
    Gia QTL; Sloan IH; Womersley RS; Wang YG, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere, http://dx.doi.org, http://arxiv.org/abs/1801.03212v1
  • Preprints | 2019
    Hamann J; Gia QTL; Sloan IH; Wang YG; Womersley RS, 2019, A New Probe of Gaussianity and Isotropy applied to the CMB Maps
    Preprints | 2019
    Wang YG; Womersley RS; Wu H-T; Yu W-H, 2019, Numerical computation of triangular complex spherical designs with small mesh ratio
    Preprints | 2018
    Gia QTL; Sloan IH; Womersley RS; Wang YG, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere
    Preprints | 2017
    Brauchart JS; Dragnev PD; Saff EB; Womersley RS, 2017, Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case
    Preprints | 2015
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2015, Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation
    Preprints | 2015
    Wang YG; Gia QTL; Sloan IH; Womersley RS, 2015, Fully discrete needlet approximation on the sphere
    Preprints | 2015
    Wang YG; Sloan IH; Womersley RS, 2015, Riemann localisation on the sphere
    Preprints | 2014
    Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2014, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces
    Preprints | 2012
    Chernih A; Sloan IH; Womersley RS, 2012, Wendland functions with increasing smoothness converge to a Gaussian
    Conference Papers | 2002
    Sloan IH; Womersley RS, 2002, 'The uniform error of hyperinterpolation on the sphere', in Haussmann W; Jetter K; Reimer M (eds.), 3rd International conference on multivariate approximation theory, WILEY-V C H VERLAG GMBH, Witten-Bommerholz, Germany, pp. 289 - 306, presented at 5th International Conference on Multivariate Approximation, Witten-Bommerholz, Germany, 22 September 2002 - 27 September 2002, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169367700020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a
    Conference Papers | 1999
    Sloan IH; Womersley RS, 1999, 'The search for good polynomial interpolation points on the sphere', in Griffiths DF; Watson GA (ed.), 18th Dundee Biennial Conference on Numerical Analysis, CHAPMAN & HALL/CRC PRESS, University of Dundee, pp. 211 - 229, presented at 18th Dundee Biennial Conference on Numerical Analysis, University of Dundee, 29 June 1999 - 02 July 1999, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000086825900011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a
    Conference Papers | 1995
    Womersley RS; Lau YK, 1995, 'Portfolio optimisation problems', in Computational Techniques and Applications: Proceedings, Computational Techniques and Applications: CTAC 1995, Singapore, presented at Computational Techniques and Applications: CTAC 1995, Singapore, 11 July 1995 - 14 July 1995
    Conference Papers | 1994
    Chen X; Womersley RS, 1994, 'A parallel inexact Newton method for stochastic programs with recourse', in Annals of Operations Research, Kluwer Academic Publ, Dordrecht, Netherlands, pp. 113 - 141, presented at IFIP Workshop, Lillehammer, Norway, http://dx.doi.org/10.1007/BF02187643