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On duality theory for non-convex semidefinite programming

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  • Wenyu Sun
  • Chengjin Li
  • Raimundo Sampaio

Abstract

In this paper, with the help of convex-like function, we discuss the duality theory for nonconvex semidefinite programming. Our contributions are: duality theory for the general nonconvex semidefinite programming when Slater’s condition holds; perfect duality for a special case of the nonconvex semidefinite programming for which Slater’s condition fails. We point out that the results of Fan (Appl. Math. Lett. 18:1068–1073, 2005 ) can be regarded as a special case of our result. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:186:y:2011:i:1:p:331-343:10.1007/s10479-011-0861-z
    DOI: 10.1007/s10479-011-0861-z
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    References listed on IDEAS

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    1. Y. J. Liu & L. W. Zhang, 2008. "Convergence of the Augmented Lagrangian Method for Nonlinear Optimization Problems over Second-Order Cones," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 557-575, December.
    2. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
    3. 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.
    4. X. M. Yang & X. Q. Yang & K. L. Teo, 2001. "Characterizations and Applications of Prequasi-Invex Functions," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 645-668, September.
    5. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
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    Cited by:

    1. Baha Alzalg & Asma Gafour, 2023. "Convergence of a Weighted Barrier Algorithm for Stochastic Convex Quadratic Semidefinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 490-515, February.

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