Derivative-free methods for nonlinear programming: constrained and noisy problems

Abstract

This research project aims to develop globally convergent algorithms for derivative-free nonlinear programming, addressing noisy problems, with algebraic and/or implicit constraints. The starting point is the class of sampling-based implicit filtering methods. A major purpose is to exploit the more appropriate features of the existing generating set search algorithms, combined with the intrinsic freedom of the implicit filtering methods, to obtain efficient and robust strategies. Another goal is to analyze the constraint qualification assumptions employed in the literature of mesh adaptive direct searches, to potentially weak them. A computational investigation will support the theoretical analysis.