Constraint Qualification and the Existence of Multipliers for Nonconvex Infinite-Dimensional Optimization Problems

Explore constraint qualification and the existence of multipliers for nonconvex infinite-dimensional optimization problems in this 29-minute conference talk by Ewa Bednarczuk. Delve into the intricacies of infinite-constrained optimization problems in Banach spaces, focusing on both equality and inequality constraints. Examine the challenges associated with Robinson and Kurcyusz-Zowe constraint qualifications, and investigate alternative regularity conditions when the derivative is not necessarily surjective. Learn about sufficient conditions for the non-emptiness of the set of Lagrange multipliers, utilizing the rank theorem and a generalization of Lusternik's theorem. Gain insights from this presentation, which was part of the "One World Optimization Seminar in Vienna" workshop held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in June 2024. Discover the collaborative research efforts of Ewa Bednarczuk, Krzysztof Leśniewski, and Krzysztof Rutkowski in advancing the field of nonconvex infinite-dimensional optimization.