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Sufficient Conditions for Global Optimality of Bivalent Nonconvex Quadratic Programs with Inequality Constraints

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Abstract

We present sufficient conditions for the global optimality of bivalent nonconvex quadratic programs involving quadratic inequality constraints as well as equality constraints. By employing the Lagrangian function, we extend the global subdifferential approach, developed recently in Jeyakumar et al. (J. Glob. Optim., 2007, to appear; Math. Program. Ser. A, 2007, to appear) for studying bivalent quadratic programs without quadratic constraints, and derive global optimality conditions.

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Authors and Affiliations

  1. Department of Mathematics, Chongqing Normal University, Chongqing, People’ Republic of China

    Z. Y. Wu

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

    V. Jeyakumar

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

    A. M. Rubinov

Authors
  1. Z. Y. Wu
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  2. V. Jeyakumar
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  3. A. M. Rubinov
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Corresponding author

Correspondence to V. Jeyakumar.

Additional information

Communicated by G. Di Pillo.

The authors are grateful to the referees for constructive comments and suggestions which have contributed to the final preparation of the paper.

Z.Y. Wu’s current address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia. The work of this author was completed while at the Department of Applied Mathematics, University of New South Wales, Sydney, Australia.

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Wu, Z.Y., Jeyakumar, V. & Rubinov, A.M. Sufficient Conditions for Global Optimality of Bivalent Nonconvex Quadratic Programs with Inequality Constraints. J Optim Theory Appl 133, 123–130 (2007). https://doi.org/10.1007/s10957-007-9177-1

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  • DOI: https://doi.org/10.1007/s10957-007-9177-1

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