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Strong Duality for General Quadratic Programs with Quadratic Equality Constraints

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  • Duy-Van Nguyen

    (University of Trier)

Abstract

In this article, by ‘general quadratic program’ we mean an optimization problem, in which all functions involved are quadratic or linear and local optima can be different from global optima. For a class of general quadratic optimization problems with quadratic equality constraints, the Lagrangian dual problem is constructed, which is a semi-infinite linear program, or equivalently, a copositive program, i.e., a conic program over the closed convex cone of copositive matrices. Solvability of both primal and dual problems and conditions for strong duality are then investigated in connection with some results from nonlinear parametric optimization.

Suggested Citation

  • Duy-Van Nguyen, 2022. "Strong Duality for General Quadratic Programs with Quadratic Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 297-313, October.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02082-3
    DOI: 10.1007/s10957-022-02082-3
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    References listed on IDEAS

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    1. N. V. Thoai, 2000. "Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 331-354, November.
    2. Joe-Mei Feng & Gang-Xuan Lin & Reuy-Lin Sheu & Yong Xia, 2012. "Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint," Journal of Global Optimization, Springer, vol. 54(2), pages 275-293, October.
    3. Flippo, Olaf E. & Jansen, Benjamin, 1996. "Duality and sensitivity in nonconvex quadratic optimization over an ellipsoid," European Journal of Operational Research, Elsevier, vol. 94(1), pages 167-178, October.
    Full references (including those not matched with items on IDEAS)

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