CONDITIONS FOR GLOBAL OPTIMALITY OF QUADRATIC MINIMIZATION PROBLEMS WITH LMI CONSTRAINTS

Vaithilingam Jeyakumar () and Zhiyou Wu ()
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Vaithilingam Jeyakumar: Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia
Zhiyou Wu: School of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China

Asia-Pacific Journal of Operational Research (APJOR), 2007, vol. 24, issue 02, 149-160

Abstract: In this paper we present sufficient conditions for global optimality of non-convex quadratic programs involving linear matrix inequality (LMI) constraints. Our approach makes use of the concept of a quadratic subgradient. We develop optimality conditions for quadratic programs with LMI constraints by using Lagrangian function and by examining conditions which minimizes a quadratic subgradient of the Lagrangian function over simple bounding constraints. As applications, we obtain sufficient optimality condition for quadratic programs with LMI and box constraints by minimizing a quadrtic subgradient over box constraints. We also give optimality conditions for quadratic minimization involving LMI and binary constraints.

Keywords: Quadratic optimization; linear matrix inequalities; box constraints; global optimality; sufficient condition; 41A65; 41A29; 90C30 (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (14)

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DOI: 10.1142/S021759590700119X

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