Algorithm for solution of convex MINLP problems

Abstract

The current work shows the fonnulation and implementation of an algorithm for the solution of convex rnixed-integer nonlinear programming (MINLP) problems. The proposed algorithm does not folJow the traditional sequence of solutions of nonlinear programming (NLP) subproblems and master mixed-integer linear programming (MILP) problems. lnstead, the mas ter problem is defined dynamically during the tree search to reduce the number of nodes that need to be enumerated. A branch and bound search is perfonned to predict lower bound by solving linear programrning (LP) subproblems until feasible integer solutions are found. For these nades, noolinear programming subproblems are olved, providing upper bounds and new linear approximations, which are used to tighten the linear representation of the open nodes in the search tree. Numerical results for convex and nonconvex test problems are analyzed, comparing the efficiency of the proposed algorithm and the general algebraic modeling system (GAMS).