Global algorithm for a class of multiplicative programs using piecewise linear approximation technique

This paper presents an efficient algorithm for solving a class of multiplicative programs (MP). For obtaining the global optimal solution of the problem (MP), we first transform the problem (MP) into the equivalent problem (EP) by introducing auxiliary variables. Next, using the new piecewise linear approximation technique, the problem (EP) is systematically converted into a series of linear relaxation programming problems (RP) for obtaining the lower bound of the optimal value for the problem (EP). Then, according to the characteristics of the problem (EP) and the structure of the branch-and-bound framework, some outer space accelerating techniques are constructed to improve the speed of the convergence of the algorithm. Furthermore, by analyzing the computational complexity of the algorithm, we give an estimation for the maximum iterations of the algorithm. Finally, numerical results are reported to demonstrate the effectiveness and robustness of the algorithm.