GLOBAL OPTIMIZATION IN GENERALIZED GEOMETRIC-PROGRAMMING

A deterministic global optimization algorithm is proposed for locating the global minimum of generalized geometric (signomial) problems (GGP ). By utilizing an exponential variable transformation the initial non convex problem (GGP) is reduced to a (DC) programming problem where bo th the constraints and the objective are decomposed into the differenc e of two convex functions. A convex relaxation of problem (DC) is then obtained based on the linear lower bounding of the concave parts of t he objective function and constraints inside some box region. The prop osed branch and bound type algorithm attains finite E-convergence to t he global minimum through the successive refinement of a convex relaxa tion of the feasible region and/or of the objective function and the s ubsequent solution of a series of nonlinear convex optimization proble ms. The efficiency of the proposed approach is enhanced by eliminating variables through monotonicity analysis, by maintaining tightly bound variables through rescaling, by further improving the supplied variab le bounds through convex minimization, and finally by transforming eac h inequality constraint so as the concave part lower bounding is as ti ght as possible. The proposed approach is illustrated with a large num ber of test examples and robust stability analysis problems. Copyright (C) 1996 Elsevier Science Ltd