Solving Multistage Mixed Nonlinear Convex Stochastic Problems

We present an algorithm to solve multistage 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 and continuous variables in all the stages. 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. Due to 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 a well-known code. Key words: stochastic programming, convex programming, branch and fix coordination, mixed integer nonlinear programming, quadratic programming, outer approximation.