Sufficient Global Optimality Conditions for Non-convex Quadratic Minimization Problems With Box Constraints

  • Authors:

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

  • Affiliations:

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

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2006

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Abstract

In this paper we establish conditions which ensure that a feasible point is a global minimizer of a quadratic minimization problem subject to box constraints or binary constraints. In particular, we show that our conditions provide a complete characterization of global optimality for non-convex weighted least squares minimization problems. We present a new approach which makes use of a global subdifferential. It is formed by a set of functions which are not necessarily linear functions, and it enjoys explicit descriptions for quadratic functions. We also provide numerical examples to illustrate our optimality conditions.