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

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 a...

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Bibliographic Details
Published in:Annals of operations research Vol. 235; no. 1; pp. 581 - 598
Main Author: Mijangos, E.
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2015
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Business and Management
Combinatorics
Convex functions
Integer programming
Mathematical analysis
Mathematical models
Mathematical research
Nonlinear programming
Nonlinearity
Operations research
Operations Research/Decision Theory
Quadratic programming
Stochastic processes
Stochasticity
Strategy
Studies
Texts
Theory of Computation
Variables
Outer approximation
Mixed-integer nonlinear programming
Quadratic programming
Convex programming
Branch-and-fix coordination method
Stochastic programming
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary: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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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-015-1899-0