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Convergence of a Weighted Barrier Algorithm for Stochastic Convex Quadratic Semidefinite Optimization

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  • Baha Alzalg

    (The University of Jordan
    The Ohio State University)

  • Asma Gafour

    (The University of Jordan
    University of Djillali Liabes)

Abstract

Mehrotra and Özevin (SIAM J Optim 19:1846–1880, 2009) computationally found that a weighted barrier decomposition algorithm for two-stage stochastic conic programs achieves significantly superior performance when compared to standard barrier decomposition algorithms existing in the literature. Inspired by this motivation, Mehrotra and Özevin (SIAM J Optim 20:2474–2486, 2010) theoretically analyzed the iteration complexity for a decomposition algorithm based on the weighted logarithmic barrier function for two-stage stochastic linear optimization with discrete support. In this paper, we extend the aforementioned theoretical paper and its self-concordance analysis from the polyhedral case to the semidefinite case and analyze the iteration complexity for a weighted logarithmic barrier decomposition algorithm for two-stage stochastic convex quadratic SDP with discrete support.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:2:d:10.1007_s10957-022-02128-6
    DOI: 10.1007/s10957-022-02128-6
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    References listed on IDEAS

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    1. Alan J. King & R. Tyrrell Rockafellar, 1993. "Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 148-162, February.
    2. Alexander Shapiro, 1993. "Asymptotic Behavior of Optimal Solutions in Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 829-845, November.
    3. Jia-Wang Nie & Ya-Xiang Yuan, 2001. "A Predictor–Corrector Algorithm for QSDP Combining Dikin-Type and Newton Centering Steps," Annals of Operations Research, Springer, vol. 103(1), pages 115-133, March.
    4. Alzalg, Baha, 2015. "Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 494-508.
    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.
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