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Journal of Global Optimization

, Volume 64, Issue 4, pp 679–702 | Cite as

Generalized Farkas’ lemma and gap-free duality for minimax DC optimization with polynomials and robust quadratic optimization

  • V. JeyakumarEmail author
  • G. M. Lee
  • N. T. H. Linh
Article

Abstract

Motivated by robust (non-convex) quadratic optimization over convex quadratic constraints, in this paper, we examine minimax difference of convex (dc) optimization over convex polynomial inequalities. By way of generalizing the celebrated Farkas’ lemma to inequality systems involving the maximum of dc functions and convex polynomials, we show that there is no duality gap between a minimax DC polynomial program and its associated conjugate dual problem. We then obtain strong duality under a constraint qualification. Consequently, we present characterizations of robust solutions of uncertain general non-convex quadratic optimization problems with convex quadratic constraints, including uncertain trust-region problems.

Keywords

Generalized Farkas’s lemma Difference of convex optimization  Minimax programs Duality Non-convex quadratic optimization Robust optimization  Convex polynomials 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of New South WalesSydneyAustralia
  2. 2.Department of Applied MathematicsPukyong National UniversityBusanKorea

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