# Duality suitable for a class of non-convex optimization problems

## TL;DR

This paper develops a duality principle applicable to many non-convex optimization problems, establishing a relation between primal and dual critical points and proving no duality gap locally.

## Contribution

It introduces a duality framework for non-convex problems using convex analysis, ensuring primal-dual critical point correspondence and gap absence.

## Key findings

- Established a duality relation for non-convex optimization
- Proved no duality gap exists locally
- Linked critical points of primal and dual problems

## Abstract

In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the critical points of the primal and dual formulations and formally prove there is no duality gap between such formulations, in a local extremal context.