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Continuity of the Solution Map in Quadratic Programs under Linear Perturbations

Author

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  • G. M. Lee

    (Pukyong National University)

  • N. N. Tam

    (Hanoi Pedagogical Institute No. 2)

  • N. D. Yen

    (Vietnamese Academy of Science and Technology)

Abstract

It is well known that the solution map of a quadratic program where only the linear part of the data is subject to perturbation is an upper Lipschitz multifunction. This paper characterizes the continuity and lower semicontinuity of that solution map.

Suggested Citation

  • G. M. Lee & N. N. Tam & N. D. Yen, 2006. "Continuity of the Solution Map in Quadratic Programs under Linear Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 415-423, June.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:3:d:10.1007_s10957-006-9076-x
    DOI: 10.1007/s10957-006-9076-x
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    References listed on IDEAS

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    2. E. Blum & W. Oettli, 1972. "Technical Note—Direct Proof of the Existence Theorem for Quadratic Programming," Operations Research, INFORMS, vol. 20(1), pages 165-167, February.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    4. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    5. B. Curtis Eaves, 1971. "On Quadratic Programming," Management Science, INFORMS, vol. 17(11), pages 698-711, July.
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    Cited by:

    1. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    2. Hoang Phu & Vo Pho, 2010. "Global infimum of strictly convex quadratic functions with bounded perturbations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 327-345, October.
    3. H. X. Phu & V. M. Pho & P. T. An, 2011. "Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 1-25, April.

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