Global and Local Quadratic Minimization |
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Authors: | M J Best B Ding |
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Institution: | (1) Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada |
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Abstract: | We present a method which when applied to certain non-convex QP will locatethe globalminimum, all isolated local minima and some of the non-isolated localminima. The method proceeds by formulating a (multi) parametric convex QP interms ofthe data of the given non-convex QP. Based on the solution of the parametricQP,an unconstrained minimization problem is formulated. This problem ispiece-wisequadratic. A key result is that the isolated local minimizers (including theglobalminimizer) of the original non-convex problem are in one-to-one correspondencewiththose of the derived unconstrained problem.The theory is illustrated with several numerical examples. A numericalprocedure isdeveloped for a special class of non-convex QP's. It is applied to a problemfrom theliterature and verifies a known global optimum and in addition, locates apreviously unknown local minimum. |
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Keywords: | Global optimization parametric quadratic programming non-convex quadratic program |
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