Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions

  • Authors:

  • V. Jeyakumar;A. M. Rubinov;Z. Y. Wu

  • Affiliations:

  • University of New South Wales, Department of Applied Mathematics, 2052, Sydney, Australia;University of Ballarat, School of Information Technology and Mathematical Sciences, 3353, Ballarat, VIC, Australia;Chongqing Normal University, Department of Mathematics, 400047, Chongqing, VIC, People’s Republic of China

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2007

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Abstract

In this paper, we first examine how global optimality of non-convex constrained optimization problems is related to Lagrange multiplier conditions. We then establish Lagrange multiplier conditions for global optimality of general quadratic minimization problems with quadratic constraints. We also obtain necessary global optimality conditions, which are different from the Lagrange multiplier conditions for special classes of quadratic optimization problems. These classes include weighted least squares with ellipsoidal constraints, and quadratic minimization with binary constraints. We discuss examples which demonstrate that our optimality conditions can effectively be used for identifying global minimizers of certain multi-extremal non-convex quadratic optimization problems.