一类非凸全局最优化问题的新的凸凹化法

PDF全文下载：2017010116

李博，杜杰

(青岛科技大学 数理学院，山东 青岛266061)

摘要：研究了一类非凸连续全局最优化问题的凸化、凹化方法。对于目标函数非凸、非凹的非线性规划，给出了一个新的凸、凹化法，通过含有参数的函数变换方法，对目标函数进行凸化或凹化，从而将原目标函数变换为相应的凸函数或凹函数，推广了凸化、凹化方法在求解非线性规划方面的应用。

关键词： 全局最优化；非线性规划；凸化；凹化

中图分类号：O 221.2文献标志码：A

引用格式：李博，杜杰.一类非凸全局最优化问题的新的凸凹化法［J］.青岛科技大学学报(自然科学版), 2017, 38(1): 116118.

LI Bo, DU Jie.A new convexification and concavification method for a class of global optimization problem［J］.Journal of Qingdao University of Science and Technology（Natural Science Edition), 2017, 38(1): 116118.

A New Convexification and Concavification Method for a Class of Global Optimization Problem

 LI Bo, DU Jie

(College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China)

Abstract: The aim of the paper is to develop convexification and concavification methods for a general class of nonconvex global optimization problem. Transformations with parameter are proposed for solving the nonlinear programming problem in which the objective function is nonconvex, nonconcave. It is shown that the original objective function can be transformed into equivalent convex or concave function by using the proposed transformation method, which extends applications of convexification and concavification schems in solving nonlinear programming problems.

 Key words: global optimization; nonlinear programming; convexification; concavification

收稿日期：   20160112

作者简介：李博(1957—),男,教授.

 文章编号：16726987（2017）01011603；DOI：10.16351/j.16726987.2017.01.020