A decomposition approach for global optimum search in QP, NLP and MINLP problems

Nonconvex programming problems are frequently encountered in engineering and operations research. A large variety of global optimization algorithms have been proposed for the various classes of programming problems. A new approach for global optimum search is presented in this paper which involves a decomposition of the variable set into two sets-complicating and noncomplicating variables. This results in a decomposition of the constraint set leading to two subproblems. The decomposition of the original problem induces special structure in the resulting subproblems and a series of these subproblems are then solved, using the Generalized Benders’ Decomposition technique, to determine the optimal solution. The key idea is to combine a judicious selection of the complicating variables with suitable transformations leading to subproblems which can attain their respective global solutions at each iteration. Mathematical properties of the proposed approach are presented. Even though the proposed approach cannot guarantee the determination of the global optimum, computational experience on a number of nonconvex QP, NLP and MINLP example problems indicates that a global optimum solution can be obtained from various starting points.