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Decomposition Based Interior Point Methods for Two-Stage Stochastic Convex Quadratic Programs with Recourse

Author

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  • Sanjay Mehrotra

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • M. Gokhan Ozevin

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

Zhao showed that the log barrier associated with the recourse function of two-stage stochastic linear programs behaves as a strongly self-concordant barrier and forms a self-concordant family on the first-stage solutions. In this paper, we show that the recourse function is also strongly self-concordant and forms a self-concordant family for the two-stage stochastic convex quadratic programs with recourse. This allows us to develop Bender's decomposition based linearly convergent interior point algorithms. An analysis of such an algorithm is given in this paper.

Suggested Citation

  • Sanjay Mehrotra & M. Gokhan Ozevin, 2009. "Decomposition Based Interior Point Methods for Two-Stage Stochastic Convex Quadratic Programs with Recourse," Operations Research, INFORMS, vol. 57(4), pages 964-974, August.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:4:p:964-974
    DOI: 10.1287/opre.1080.0659
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    References listed on IDEAS

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    Cited by:

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    2. Kuang-Yu Ding & Xin-Yee Lam & Kim-Chuan Toh, 2023. "On proximal augmented Lagrangian based decomposition methods for dual block-angular convex composite programming problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 117-161, September.
    3. Cosmin Petra & Mihai Anitescu, 2012. "A preconditioning technique for Schur complement systems arising in stochastic optimization," Computational Optimization and Applications, Springer, vol. 52(2), pages 315-344, June.

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