Parametric optimization for the Lipschitz function

Simplicial Lipschitz optimization without the Lipschitz constant

In this paper we propose a new simplicial partition-based deterministic algorithm for global optimization of Lipschitz-continuous functions without requiring any knowledge of the Lipschitz constant. Our algorithm is motivated by the well-known Direct algorithm which evaluates the objective function on a set of points that tries to cover the most promising subregions of the feasible region. Almo...

Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability

This paper is devoted to the study of the stability of the solution map for the parametric convex semi-infinite optimization problem under convex function perturbations in short, PCSI. We establish sufficient conditions for the pseudo-Lipschitz property of the solution map of PCSI under perturbations of both objective function and constraint set. The main result obtained is new even when the pr...

Global optimization of Lipschitz functions

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO wh...

Exact Barrier Function Methods for Lipschitz Programs

The purposeof this paper is twofold. First we considera class of nondiierentiablepenaltyfunctions for constrained Lipschitz programs and then we show how these penalty functions can be employed to actually solve a constrained Lipschitz program. The penalty functions considered incorporate a barrier term which makes their value go to innnity on the boundary of a perturbation of the feasible set....

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients