Mangasarian-Fromovitz-type constraint qualification and optimality conditions for smooth infinite programming problems

TL;DR

This paper introduces a new constraint qualification (GPMFCQ) for smooth infinite programming problems, generalizing previous conditions, and proves the existence of Lagrange multipliers under this framework.

Contribution

It proposes a novel constraint qualification for infinite programming and establishes conditions for the existence of Lagrange multipliers.

Findings

GPMFCQ generalizes PMFCQ for infinite problems.

Existence of Lagrange multipliers proven under GPMFCQ.

Uses Hurwicz set and Nonlinear Farkas Minkowski condition.

Abstract

We introduce a constraint qualification condition (GPMFCQ) for smooth infinite programming problems, where the nonlinear operator defining the equality constraints has nonsurjective derivative at the local minimum. The condition is a generalization of PMFCQ introduced by Morduhovich and Nghia. We prove the existence of Lagrange multipliers by using either Hurwicz set or Nonlinear Farkas Minkowski condition.