Prof. Boris S. Mordukhovich
Wayne State University, Detroit, USA
Derivative-Free Methods in Nonconvex Optimization
Abstract. This talk discusses some new directions and results for models of derivative-free optimization (DFO) with nonconvex data. We overview several approaches to DFO problems and focus on finite-difference approximation schemes. Our algorithms address the two major classes: objective functions with globally Lipschitzian and locally Lipschitzian gradients, respectively. Global convergence results with constructive convergence rates are established for both cases in noiseless and noisy environments. The developed algorithms in the noiseless case are based on the backtracking linesearch and achieves fundamental convergence properties. The noisy version is essentially more involved being bases on the novel dynamic step linearsearch. Numerical experiments demonstrate higher robustness of the proposed algorithms compared with other finite-difference-based schemes.
