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An algorithm for two-stage stochastic mixed-integer nonlinear convex problems

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  • E. Mijangos

Abstract

We present an algorithm to solve two-stage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0–1 mixed-integer recourse variables in the first stage and only continuous variables in the second stage. The non-anticipativity constraints are satisfied by means of the twin-node-family strategy. In this work to solve each nonlinear convex subproblem at each node we propose the solution of sequences of quadratic subproblems. Since the convexity of the constraints we can approximate them by means of outer approximations. These methods have been implemented in C $$++$$ + + with the help of Cplex 12.1, which only solves the quadratic approximations. The test problems have been randomly generated by using a C $$++$$ + + code developed by this author. Numerical experiments have been performed and its efficiency has been compared with that of well-known codes. Copyright Springer Science+Business Media New York 2015

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  • E. Mijangos, 2015. "An algorithm for two-stage stochastic mixed-integer nonlinear convex problems," Annals of Operations Research, Springer, vol. 235(1), pages 581-598, December.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:581-598:10.1007/s10479-015-1899-0
    DOI: 10.1007/s10479-015-1899-0
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    References listed on IDEAS

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    1. Alonso-Ayuso, A. & Escudero, L. F. & Garín, A. & Ortuño, M. T. & Pérez, G., 2005. "On the product selection and plant dimensioning problem under uncertainty," Omega, Elsevier, vol. 33(4), pages 307-318, August.
    2. Gilbert Laporte & FranÇois V. Louveaux & Luc van Hamme, 2002. "An Integer L -Shaped Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 50(3), pages 415-423, June.
    3. Escudero, L.F. & Garín, M.A. & Merino, M. & Pérez, G., 2010. "An exact algorithm for solving large-scale two-stage stochastic mixed-integer problems: Some theoretical and experimental aspects," European Journal of Operational Research, Elsevier, vol. 204(1), pages 105-116, July.
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    Cited by:

    1. Can Li & Ignacio E. Grossmann, 2019. "A generalized Benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary first and second stage variables," Journal of Global Optimization, Springer, vol. 75(2), pages 247-272, October.
    2. Unai Aldasoro & María Merino & Gloria Pérez, 2019. "Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic," Annals of Operations Research, Springer, vol. 280(1), pages 151-187, September.
    3. Manish Bansal & Yingqiu Zhang, 2021. "Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs," Journal of Global Optimization, Springer, vol. 81(2), pages 391-433, October.
    4. Can Li & Ignacio E. Grossmann, 2019. "A finite $$\epsilon $$ϵ-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables," Journal of Global Optimization, Springer, vol. 75(4), pages 921-947, December.

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