G-coupling functions: The Infinite Dimensional case

TL;DR

This paper introduces G-coupling functions, a new class inspired by gap functions, which facilitate duality schemes in infinite-dimensional minimization problems through general conjugation theory.

Contribution

It presents G-coupling functions and demonstrates their role in creating duality schemes and Lagrange-type functions in infinite-dimensional optimization.

Findings

G-coupling functions can generate duality schemes in infinite-dimensional spaces

A Lagrange-type function is constructed using G-coupling functions

The approach extends conjugation theory to new classes of optimization problems

Abstract

In this work we present a class of functions, motivated by gap functions, which we call G-coupling functions. We will show that these functions can generate a duality scheme for minimization problems by means of the general conjugation theory. Thanks to this scheme, a Lagrange-type function is introduced as well.