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 nonconvex problem (GGP) is reduced to a (DC) programming problem where both the constraints and the objective are decomposed into the diierence of two convex functions. A convex relaxation of problem (DC) is then obtained based on the linear lower bounding of the concave parts of the objective function and constraints inside some box region. The proposed branch and bound type algorithm attains nite {convergence to the global minimum through the successive reenement of a convex relaxation of the feasible region and/or of the objective function and the subsequent solution of a series of nonlinear convex optimization problems. The eeciency of the proposed approach is enhanced by eliminating variables through monotonicity analysis, by maintaining tightly bound variables through rescaling, by further improving the supplied variable bounds through convex minimization, and nally by transforming each inequality constraint so as the concave part lower bounding is as tight as possible. The proposed approach is illustrated with a large number of test examples and robust stability analysis problems.