# A duality principle for non-convex optimization in $\mathbb{R}^n$

## TL;DR

This paper introduces a duality principle for certain non-convex optimization problems in al R^n, establishing conditions for optimality and the absence of duality gap using convex analysis and D.C. optimization techniques.

## Contribution

It develops a duality framework for non-convex problems, extending classical convex analysis tools and proving no duality gap at local extremal points.

## Key findings

- Established a duality principle for non-convex optimization in al R^n.
- Derived global sufficient optimality conditions.
- Proved the absence of duality gap at local extremal points.

## Abstract

This article develops a duality principle for a class of optimization problems in $\mathbb{R}^n$. The results are obtained based on standard tools of convex analysis and on a well known result of Toland for D.C. optimization. Global sufficient optimality conditions are also presented as well as relations between the critical points of the primal and dual formulations. Finally we formally prove there is no duality gap between the primal and dual formulations in a local extremal context.