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Canonical Dual Solutions to Quadratic Optimization over One Quadratic Constraint

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wenxun Xing & Shu-Cherng Fang & Ruey-Lin Sheu & Liping Zhang, 2015. "Canonical Dual Solutions to Quadratic Optimization over One Quadratic Constraint," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(01), pages 1-21.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:01:n:s0217595915400072
    DOI: 10.1142/S0217595915400072
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