Canonical Dual Solutions to Quadratic Optimization over One Quadratic Constraint

Wenxun Xing (), Shu-Cherng Fang (), Ruey-Lin Sheu () and Liping Zhang ()
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Wenxun Xing: Department of Mathematical Sciences, Tsinghua University, Beijing, China
Shu-Cherng Fang: Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA
Ruey-Lin Sheu: Department of Mathematics, National Cheng Kung University, Taiwan
Liping Zhang: Department of Mathematical Sciences, Tsinghua University, Beijing, China

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 01, 1-21

Abstract: A quadratic optimization problem with one nonconvex quadratic constraint is studied using the canonical dual approach. Under the dual Slater's condition, we show that the canonical dual has a smooth concave objective function over a convex feasible domain, and this dual has a finite supremum unless the original quadratic optimization problem is infeasible. This supremum, when it exists, always equals to the minimum value of the primal problem. Moreover, a global minimizer of the primal problem can be provided by a dual-to-primal conversion plus a "boundarification" technique. Application to solving a quadratic programming problem over a ball is included and an error bound estimation is provided.

Keywords: Non-convex quadratic programming; canonical duality; Slater's condition; error bound analysis (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0217595915400072

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