Using conical partition to globally maximizing the nonlinear sum of ratios |
| |
Authors: | Peiping Shen Li Jin |
| |
Affiliation: | 1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, PR China;2. Basic Course Department, Henan Mechanical and Electrical Engineering College, Xinxiang 453002, PR China |
| |
Abstract: | This article presents a global optimization algorithm for globally maximizing the sum of concave–convex ratios problem with a convex feasible region. The algorithm uses a branch and bound scheme where a concave envelope of the objective function is constructed to obtain an upper bound of the optimal value by using conical partition. As a result, the upper-bound subproblems during the algorithm search are all ordinary convex programs with less variables and constraints and do not grow in size from iterations to iterations in the computation procedure, and furthermore a new bounding tightening strategy is proposed such that the upper-bound convex relaxation subproblems are closer to the original nonconvex problem to enhance solution procedure. At last, some numerical examples are given to vindicate our conclusions. |
| |
Keywords: | Global optimization Sum of ratios Branch-and-bound Concave envelope Bounding tightening strategy |
本文献已被 ScienceDirect 等数据库收录! |
|