A New Approach to Yakubovich's s-Lemma

Abstract

Subject to regularity assumptions, Yakubovich's s-Lemma characterizes the quadratic functions f(x) defined on a finite-dimensional space which are copositive with a given quadratic function q(x). This result has far-reaching consequences in optimization and control theory. Several approaches to its proof are known, some of which generalize to Hilbert spaces. In this paper we explore a new geometric approach to the proof of this classical result