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Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming

Author

Listed:
  • N. Dinh

    (University of Pedagogy
    Pukyong National University)

  • V. Jeyakumar

    (University of New South Wales)

  • G. M. Lee

    (Pukyong National University)

Abstract

In this paper it is shown that, in the absence of any regularity condition, sequential Lagrangian optimality conditions as well as a sequential duality results hold for abstract convex programs. The significance of the results is that they yield the standard optimality and duality results for convex programs under a simple closed-cone condition that is much weaker than the well-known constraint qualifications. As an application, a sequential Lagrangian duality, saddle-point conditions, and stability results are derived for convex semidefinite programs.

Suggested Citation

  • N. Dinh & V. Jeyakumar & G. M. Lee, 2005. "Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 85-112, April.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:1:d:10.1007_s10957-004-1712-8
    DOI: 10.1007/s10957-004-1712-8
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    Citations

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    Cited by:

    1. N. Dinh & G. Vallet & M. Volle, 2014. "Functional inequalities and theorems of the alternative involving composite functions," Journal of Global Optimization, Springer, vol. 59(4), pages 837-863, August.
    2. N. Dinh & V. Jeyakumar, 2014. "Farkas’ lemma: three decades of generalizations for mathematical optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 1-22, April.
    3. N. Dinh & M. A. Goberna & M. A. López & T. H. Mo, 2017. "Farkas-Type Results for Vector-Valued Functions with Applications," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 357-390, May.
    4. T. Q. Son & J. J. Strodiot & V. H. Nguyen, 2009. "ε-Optimality and ε-Lagrangian Duality for a Nonconvex Programming Problem with an Infinite Number of Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 389-409, May.
    5. Wenyu Sun & Chengjin Li & Raimundo Sampaio, 2011. "On duality theory for non-convex semidefinite programming," Annals of Operations Research, Springer, vol. 186(1), pages 331-343, June.
    6. N. Dinh & J. Strodiot & V. Nguyen, 2010. "Duality and optimality conditions for generalized equilibrium problems involving DC functions," Journal of Global Optimization, Springer, vol. 48(2), pages 183-208, October.

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