Farkas’ lemma: three decades of generalizations for mathematical optimization

In this paper we present a survey of generalizations of the celebrated Farkas’s lemma, starting from systems of linear inequalities to a broad variety of non-linear systems. We focus on the generalizations which are targeted towards applications in continuous optimization. We also briefly describe the main applications of generalized Farkas’ lemmas to continuous optimization problems. Copyright Sociedad de Estadística e Investigación Operativa 2014