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

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.

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Acknowledgments

This research has been partially supported by the grant MTM2013-48462-C2-1-R of the Spanish research program.

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Correspondence to E. Mijangos.

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Mijangos, E. An algorithm for two-stage stochastic mixed-integer nonlinear convex problems. Ann Oper Res 235, 581–598 (2015). https://doi.org/10.1007/s10479-015-1899-0

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Keywords

  • Stochastic programming
  • Convex programming
  • Branch-and-fix coordination method
  • Mixed-integer nonlinear programming
  • Quadratic programming
  • Outer approximation