Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions |
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Authors: | V Jeyakumar A M Rubinov Z Y Wu |
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Institution: | (1) Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia;(2) Present address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, 3353, VIC, Australia;(3) Department of Mathematics, Chongqing Normal University, Chongqing, 400047, People’s Republic of China |
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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.
The work of Z. Y. Wu was carried out while the author was at the Department of Applied Mathematics, University of New South
Wales, Sydney, Australia. |
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Keywords: | Non-convex quadratic minimization Global optimality conditions Lagrange multipliers Quadratic inequality constraints Binary constraints |
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