A Derivative-free VU-algorithm for Convex Nonsmooth Minimisation

Abstract:

The VU-algorithm is a superlinearly convergent method for minimising nonsmooth convex functions. At each iteration, the algorithm separates the space into the V-space and the orthogonal U-space, such that the nonsmoothness of the objective function is concentrated on its projection onto the V-space, and on the U-space the projection is smooth. This structure allows for an alternation between a Newton-like step parallel to the U-space, and a proximal-point step parallel to the V-space. This work establishes a derivative-free variant of the VU-algorithm for convex finite-max objective functions. Global convergence is proved and numerical results are provided, demonstrating the feasibility and practical value of the approach.

Dr. Chayne Planiden specialises in nonsmooth optimisation and regularisation, as well as derivative-free methods. He obtained his Ph.D. from UBC in Canada, and he now works at UOW in Wollongong and Liverpool. His research interests include Moreau envelopes, proximal mappings and prox-regular functions in Convex and Nonconvex Analysis, nonsmooth optimisation algorithms such as VU, and DFO methods.