A GLOBAL OPTIMIZATION ALGORITHM (GOP) FOR CERTAIN CLASSES OF NONCONVEX NLPS .2. APPLICATION OF THEORY AND TEST PROBLEMS

In Part I (Floudas and Visweswaran, Computers chem. Engng 14, 1397, 1990), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the rigorous solution of the problem through a series of primal and relaxed dual problems until the upper and lower bounds from these problems converged to an epsilon-global optimum. In this paper, theoretical results are presented for several classes of mathematical programming problems that include: (i) the general quadratic programming problem; (ii) quadratic programming problems with quadratic constraints; (iii) pooling and blending problems; and (iv) unconstrained and constrained optimization problems with polynomial terms in the objective function and/or constraints. For each class, a few examples are presented illustrating the approach.