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Perturbing the Dual Feasible Region for Solving Convex Quadratic Programs

Author

Listed:
  • S. C. Fang

    (North Carolina State University)

  • H. S. J. Tsao

    (University of California)

Abstract

A dual l p-norm perturbation approach is introduced for solving convex quadratic programming problems. The feasible region of the Lagrangian dual program is approximated by a proper subset that is defined by a single smooth convex constraint involving the l p-norm of a vector measure of constraint violation. It is shown that the perturbed dual program becomes the dual program as p→∞ and, under some standard conditions, the optimal solution of the perturbed dual program converges to a dual optimal solution. A closed-form formula that converts an optimal solution of the perturbed dual program into a feasible solution of the primal convex quadratic program is also provided. Such primal feasible solutions converge to an optimal primal solution as p→∞. The proposed approach generalizes the previously proposed primal perturbation approach with an entropic barrier function. Its theory specializes easily for linear programming.

Suggested Citation

  • S. C. Fang & H. S. J. Tsao, 1997. "Perturbing the Dual Feasible Region for Solving Convex Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 73-85, July.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022655502360
    DOI: 10.1023/A:1022655502360
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    Cited by:

    1. Da Tian, 2015. "An exterior point polynomial-time algorithm for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 61(1), pages 51-78, May.

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