Image Space Accelerating Algorithm for Solving a Class of Multiplicative Programming Problems

This paper interprets an image space accelerating branch and bound algorithm for globally solving a class of multiplicative programming problems (MP). In this algorithm, in order to obtain the global optimal solution, the problem (MP) is transformed into an equivalent problem (P2) by introducing new variables. By utilizing new linearizing relaxation technique, the problem (P2) can be converted into a series of linear relaxation programming problems, which provide the reliable lower bound in the branch and bound search. Meanwhile, an image space accelerating method is constructed to improve the computational performance of the algorithm by deleting the subintervals which have no global optimal solution. Furthermore, the global convergence of the algorithm is proved. The computational complexity of the algorithm is analyzed, and the maximum iterations of the algorithm are estimated. Finally, numerical experimental results show that the algorithm is robust and efficient.