| 互补约束数学规划问题的一个广义梯度投影罚算法 |
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| 引用本文： | 黎健玲,黄小津,简金宝,唐春明.互补约束数学规划问题的一个广义梯度投影罚算法[J].数学年刊A辑(中文版),2015,36(3):277-290. |
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| 作者姓名： | 黎健玲 黄小津 简金宝 唐春明 |
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| 作者单位： | 广西大学数学与信息科学学院, 南宁 530004.,广西大学数学与信息科学学院, 南宁 530004.,通讯作者. 玉林师范学院数学与信息科学学院, 广西高校复杂系统优化与大数据处理重点实验室, 广西 玉林 537000.,广西大学数学与信息科学学院, 南宁 530004. |
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| 基金项目： | 本文受到国家自然科学基金 (No.11271086), 广西自然科学基金 (No.2012GXNSFAA053007, No.2014 GXSFFA118001),
广西高等学校重点资助科研项目 (No.201102ZD002)和广西硕士研究生科研创新项目 (No.YCXZ2013011)的资助. |
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| 摘 要： | 结合罚函数思想和广义梯度投影技术,提出求解非线性互补约束数学规划问题的一个广义梯度投影罚算法.首先,通过扰动技术和广义互补函数,将原问题转化为序列带参数的近似的标准非线性规划;其次,利用广义梯度投影矩阵构造搜索方向的显式表达式.一个特殊的罚函数作为效益函数,而且搜索方向能保证效益函数的下降性.在适当的假设条件下算法具有全局收敛性.
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| 关 键 词： | 非线性互补约束 数学规划问题 广义梯度投影 全局收敛性 |
A Generalized Gradient Projection Penalty Algorithm
for Mathematical Programming Problems with
Complementarity Constraints |
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| LI Jianling,HUANG Xiaojin,JIAN Jinbao and TANG Chunming.A Generalized Gradient Projection Penalty Algorithm
for Mathematical Programming Problems with
Complementarity Constraints[J].Chinese Annals of Mathematics,2015,36(3):277-290. |
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| Authors: | LI Jianling HUANG Xiaojin JIAN Jinbao and TANG Chunming |
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| Institution: | College of Mathematics and Information Science, Guangxi University, Nanning
530004, China.,College of Mathematics and Information Science, Guangxi University, Nanning
530004, China.,Corresponding author. School of Mathematics and Information Science,
Guangxi Colleges and Universities Key Lab of Complex System Optimization
and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi,
China. and College of Mathematics and Information Science, Guangxi University, Nanning
530004, China. |
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| Abstract: | In this paper, combining with the ideas of penalty functions and the techniques
of generalized gradient projection, a generalized gradient projection penalty algorithm is
presented for mathematical programming problems with nonlinear complementarity con-
straints. The authors first transform the investigated problem into sequential parametric
approximate standard nonlinear programs by perturbed techniques and a generalized com-
plementarity function. Then by means of a generalized gradient projection matrix, an ex-
plicit formula is constructed for search directions. A special penalty function is used as the
merit function, and the search directions ensure the descent of the merit function. Under
some mild conditions, the proposed algorithm is proven to be globally convergent. |
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| Keywords: | Nonlinear complementarity constraints Mathematical program-
ming problems Generalized gradient projection Global conver-
gence |
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