, Volume 22, Issue 1, pp 1–22 | Cite as

Farkas’ lemma: three decades of generalizations for mathematical optimization

  • N. DinhEmail author
  • V. Jeyakumar
Invited Paper


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.


Generalized Farkas’ lemma Optimality Duality Mathematical optimization 

Mathematics Subject Classification (2000)

90C60 90C56 90C26 


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© Sociedad de Estadística e Investigación Operativa 2014

Authors and Affiliations

  1. 1.Department of MathematicsInternational University Vietnam National University-Ho Chi Minh CityHo Chi Minh CityVietnam
  2. 2.Department of Applied MathematicsUniversity of New South WalesSydneyAustralia

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