A BRANCH-AND-BOUND REDUCED ALGORITHM FOR SOLVING A CLASS OF LINEAR MULTIPLICATIVE PROGRAMMING PROBLEMS
Gao Yuelin1,2, Jing Xia3
1. Institute of Information and System Science, Beifang University for Nationalities, Yinchuan 750021, China;
2. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China;
3. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China
A branch-and-bound reduced method is proposed for globally solving a class of linear multiplicative programming problems and the convergence of the algorithm is proved. In this algorithm, the lower bound functions on the multiplications in the constraints and the objective functions are given by using the convex envelopes technique of the two-vector multiplications so as to determine a relaxed convex programming of the original problem. We solve the relaxed convex programming to find the global optimization value's lower bound the feasible solutions of the original problem.In order to improve convergence rate, a rectangular reduction strategy is used. Numerical experiments show that the proposed algorithm is feasible.