Global Optimization for the Concave-Concave Multiplicative Programming with Coefficient

In this paper, we present a global optimization algorithm for globally solving the problem (CMPC) of minimizing a concave-concave multiplicative function with coefficient over a compact convex set. We firstly convert problem (CMPC) into an equivalent programming problem (CMPC(H)) by introducing 2p auxiliary variables. By utilizing the llinearization technique, initial non-convex nonlinear problem (CMPC) is reduced to a sequence of convex programming problems through the successive refinement of a linear relaxation of feasible region and of the objective function. It has been proved that the algorithm possesses global convergence. Some numerical examples are given to illustrate validity of the proposed method.