Unifying Farkas lemma and S-lemma: new theory and applications in nonquadratic nonconvex optimization

TL;DR

This paper unifies the nonlinear Farkas lemma and S-lemma into a generalized theorem, enabling new approaches to solve complex nonconvex, non-quadratic optimization problems by uncovering hidden convexity.

Contribution

It introduces a unified theoretical framework that extends classical lemmas to nonlinear nonconvex systems, facilitating global optimization solutions.

Findings

Unified nonlinear Farkas and S-lemma into a generalized alternative theorem

Revealed hidden convexity in nonconvex non-quadratic optimization problems

Enabled new methods for globally solving complex optimization problems

Abstract

We unify nonlinear Farkas lemma and S-lemma to a generalized alternative theorem for nonlinear nonconvex system. It provides fruitful applications in globally solving nonconvex non-quadratic optimization problems via revealing the hidden convexity.