| 引用本文： |
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韦增欣,赵岩,陈翠玲.利用Fisher函数解约束优化问题的广义梯度投影算法[J].广西科学,2006,13(2):102-104. [点击复制]
- WEI Zeng-xin,ZHAO Yan,CHEN Cui-ling.A Generalized Gradient Projection Algorithm with the Fisher Function for Solving the Constrained Optimization Problem[J].Guangxi Sciences,2006,13(2):102-104. [点击复制]
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| 摘要: |
| 通过引入一个辅助优化问题,将广义投影与罚函数技巧和Fisher函数ϕ(a,b)=√a2+b2-(a+b),a,b∈En的特殊性质:√a2+b2-(a+b)=0⇔a ≥ 0,b ≥ 0,ab=0结合起来,给出处理非线性等式、不等式约束问题的广义梯度投影算法,并证明该算法是全局收敛的.该算法不仅保持文献[6]的优点,而且还扩大了初始点的选择范围. |
| 关键词: 约束优化 梯度投影 罚函数 Fisher函数 全局收敛性 |
| DOI： |
| 投稿时间：2005-05-27 |
| 基金项目:国家自然科学基金(10161002);广西自然科学基金(30542043)资助 |
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| A Generalized Gradient Projection Algorithm with the Fisher Function for Solving the Constrained Optimization Problem |
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WEI Zeng-xin, ZHAO Yan, CHEN Cui-ling
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| (College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| In this paper, we give a generalized gradient projection algorithm for solving equality and inequality constrained optimization problem by introducing an assistant optimization problem and combining the following three facets:1) generalized projection, 2) the sbill of penalty function, 3) Fisher function ϕ (a, b)=√a2+b2- (a+b), which has its special property:√a2+b2- (a+b)=0⇔a ≥ 0, b ≥ 0, ab=0.Furthermore, we prove that this algorithm is globally convergent.This algorithm preserves not only the advantage of reference[6], but also extends the choice range of initial point. |
| Key words: constrained optimization gradient projection penalty function Fisher function global convergence |
