A Note on Duality in Reverse Convex Optimization

TL;DR

This paper investigates the duality theory in reverse convex optimization problems, focusing on cases with infinite inequality constraints without additional topological or measure-theoretic assumptions.

Contribution

It extends duality analysis in reverse convex optimization to the general case with infinite constraints lacking extra structure.

Findings

Duality principles are established for infinite reverse convex constraints.

Results apply without assuming topological or measure-theoretic structures.

The work clarifies conditions under which duality holds in complex reverse convex problems.

Abstract

In this note we explore duality in reverse convex optimization with reverse convex inequality constraints. While we are examining the special case of a finite index set of the inequality constraints, we are primarily interested in the general case of an arbitrary infinite index set with neither extra topological structure nor extra measure structure.