改进的凝聚约束同伦方法求解一类非线性最优化问题

改进的凝聚约束同伦方法求解一类非线性最优化问题

苏孟龙1, 赵立芹2, 吕显瑞3

1. 洛阳师范学院数学学院, 河南洛阳 471000; 2. 吉林大学学报编辑部, 长春 130021; 3. 吉林大学数学学院, 长春 130012

收稿日期:2008-09-17 修回日期:1900-01-01 出版日期:2008-11-26 发布日期:2008-11-26
通讯作者: 苏孟龙

Modified Aggregate Constraint Homotopy Method to Solvea Class of Nonlinear Optimization Problem

SU Menglong1, ZHAO Liqin2, L Xianrui3

1. College of Mathematics, Luoyang Normal University, Luoyang 471000, Henan Province, China;2. Editorial Department of Journal of Jilin University, Changchun 130021, China;3. College of Mathematics, Jilin University, Changchun 130012, China

Received:2008-09-17 Revised:1900-01-01 Online:2008-11-26 Published:2008-11-26
Contact: SU Menglong

摘要/Abstract

摘要： 利用凝聚函数的一个等价形式, 提出一种改进的凝聚约束同伦方法, 使得初始可行域包含原问题的可行域, 并从外部逐渐逼近原问题的可行域, 从而克服了凝聚约束同伦方法可能无法求得一些可行域边界附近K-K-T点的问题. 改进的凝聚约束同伦法还扩大了初始点的选择范围.

关键词: 凝聚约束同伦方法, 非线性最优化问题, 初始点

Abstract: On the basis of an equivalent form of the aggregate function, we proposed the modified aggregate constraint homotopy method, which makes the initial parameterized feasible set contain and approach the feasibleset of the original nonlinear optimization problems from the exterior as the parameter reduces to 0. Hence the modified aggregate constraint homotopy method can solve the K-K-T point close to the boundary of the feasible set, as the aggregate constraint homotopy method may not solve. Moreover, the modified aggregate constraint homotopy method also enlarges the choice scope of the initial point.

Key words: aggregate constraint homotopy method, nonlinear optimization problem, initial point

中图分类号:

O221.2

苏孟龙1, 赵立芹2, 吕显瑞3. 改进的凝聚约束同伦方法求解一类非线性最优化问题[J]. J4, 2008, 46(06): 1094-1096.

SU Menglong1, ZHAO Liqin2, L Xianrui3. Modified Aggregate Constraint Homotopy Method to Solvea Class of Nonlinear Optimization Problem[J]. J4, 2008, 46(06): 1094-1096.