Abstract
We consider a branch‐and‐reduce approach for solving generalized linear multiplicative programming. First, a new lower approximate linearization method is proposed; then, by using this linearization method, the initial nonconvex problem is reduced to a sequence of linear programming problems. Some techniques at improving the overall performance of this algorithm are presented. The proposed algorithm is proved to be convergent, and some experiments are provided to show the feasibility and efficiency of this algorithm.
Highlights
It is well known that the product of affine functions need not be quasi convex, the problem can have multiple locally optimal solutions, many of which fail to be globally optimal, that is, problem P is multiextremal 5
Many solution algorithms have been proposed for globally solving special forms of P. They can be generally classified as outer-approximation method 6, decomposition method 7, finite branch and bound algorithms 8, 9, and cutting plane method 10
The global optimization algorithms based on the general form P have been little studied
Summary
The following generalized linear multiplicative programming is considered: min p0. The aim of this paper is to provide a new branch-and-reduce algorithm for globally solving problem P. The main features of this algorithm: 1 the problem investigated in this paper has a more general form than those in 6–10 ; 2 a new linearization method for solving the problem Q is proposed; 3 these generated linear relaxation programming problems are embedded within a branch and bound algorithm without increasing the number of variables and constraints; 4 some techniques are proposed to improve the convergence speed of our algorithm.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
