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Extended trust-region problems with one or two balls: exact copositive and Lagrangian relaxations

Immanuel Bomze, Vaithilingam Jeyakumar and Guoyin Li
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Vaithilingam Jeyakumar: University of New South Wales
Guoyin Li: University of New South Wales

Journal of Global Optimization, 2018, vol. 71, issue 3, No 8, 569 pages

Abstract: Abstract We establish a geometric condition guaranteeing exact copositive relaxation for the nonconvex quadratic optimization problem under two quadratic and several linear constraints, and present sufficient conditions for global optimality in terms of generalized Karush–Kuhn–Tucker multipliers. The copositive relaxation is tighter than the usual Lagrangian relaxation. We illustrate this by providing a whole class of quadratic optimization problems that enjoys exactness of copositive relaxation while the usual Lagrangian duality gap is infinite. Finally, we also provide verifiable conditions under which both the usual Lagrangian relaxation and the copositive relaxation are exact for an extended CDT (two-ball trust-region) problem. Importantly, the sufficient conditions can be verified by solving linear optimization problems.

Keywords: Copositive matrices; Non-convex optimization; Quadratic optimization; Quadratically constrained problem; Global optimality condition; Relaxation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10898-018-0607-4

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