Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints

no code implementations • 3 Nov 2018 • Coralia Cartis, Nick I. M. Gould, Philippe L. Toint

We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i. e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected) constraints, if any, is negligible compared to that of evaluating the objective function.

Exploiting problem structure in derivative free optimization

1 code implementation • 14 Jan 2020 • Margherita Porcelli, Philippe L. Toint

A structured version of derivative-free random pattern search optimization algorithms is introduced which is able to exploit coordinate partially separable structure (typically associated with sparsity) often present in unconstrained and bound-constrained optimization problems.

Optimization and Control 65K05, 90C56, 90C90

A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks

no code implementations • 23 May 2023 • Serge Gratton, Valentin Mercier, Elisa Riccietti, Philippe L. Toint

Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems.