A new linearization method for generalized linear multiplicative programming

2011 ◽  
Vol 38 (7) ◽  
pp. 1008-1013 ◽  
Author(s):  
Chun-Feng Wang ◽  
San-Yang Liu
Keyword(s):  
Linearization Method ◽  
Multiplicative Programming ◽  
Linear Multiplicative Programming

scholarly journals Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Chun-Feng Wang ◽  
Yan-Qin Bai
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Algorithm ◽  
Linearization Method ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Global Optimization Algorithm ◽  
Multiplicative Programming ◽  
Linear Multiplicative Programming ◽  
Pruning Techniques

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm.

scholarly journals A Branch-and-Reduce Approach for Solving Generalized Linear Multiplicative Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Chun-Feng Wang ◽  
San-Yang Liu ◽  
Geng-Zhong Zheng
Keyword(s):  
Linear Programming ◽  
Linearization Method ◽  
Multiplicative Programming ◽  
Nonconvex Problem ◽  
Linear Multiplicative Programming ◽  
Linear Programming Problems ◽  
Overall Performance ◽  
Approximate Linearization

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.

scholarly journals An Efficient Outer Space Algorithm for Generalized Linear Multiplicative Programming Problem

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 80629-80637 ◽  
Author(s):  
Hongwei Jiao ◽  
Wenjie Wang ◽  
Rongjiang Chen ◽  
Youlin Shang ◽  
Jingben Yin
Keyword(s):  
Programming Problem ◽  
Outer Space ◽  
Multiplicative Programming ◽  
Linear Multiplicative Programming

scholarly journals Global Optimization for Generalized Linear Multiplicative Programming Using Convex Relaxation

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yingfeng Zhao ◽  
Ting Zhao
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Recent Literature ◽  
Convex Relaxation ◽  
Relaxation Method ◽  
Engineering Practice ◽  
Multiplicative Programming ◽  
Wide Range ◽  
Linear Multiplicative Programming ◽  
Convergence And Optimality

Applications of generalized linear multiplicative programming problems (LMP) can be frequently found in various areas of engineering practice and management science. In this paper, we present a simple global optimization algorithm for solving linear multiplicative programming problem (LMP). The algorithm is developed by a fusion of a new convex relaxation method and the branch and bound scheme with some accelerating techniques. Global convergence and optimality of the algorithm are also presented and extensive computational results are reported on a wide range of problems from recent literature and GLOBALLib. Numerical experiments show that the proposed algorithm with a new convex relaxation method is more efficient than usual branch and bound algorithm that used linear relaxation for solving the LMP.

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