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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia

    V. Jeyakumar

  2. School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, 3353, Victoria, Australia

    A. M. Rubinov

  3. Department of Mathematics, Chongqing Normal University, Chongqing, 400047, People’s Republic of China

    Z. Y. Wu

Authors
  1. V. Jeyakumar
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  2. A. M. Rubinov
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  3. Z. Y. Wu
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Correspondence to V. Jeyakumar.

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Jeyakumar, V., Rubinov, A.M. & Wu, Z.Y. Sufficient Global Optimality Conditions for Non-convex Quadratic Minimization Problems With Box Constraints. J Glob Optim 36, 471–481 (2006). https://doi.org/10.1007/s10898-006-9022-3

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  • DOI: https://doi.org/10.1007/s10898-006-9022-3

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