| 非线性互补约束规划的一个广义强次可行方向算法 |
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| 引用本文： | 简金宝,覃义,梁玉梅.非线性互补约束规划的一个广义强次可行方向算法[J].高等学校计算数学学报,2007,29(1):15-27. |
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| 作者姓名： | 简金宝 覃义 梁玉梅 |
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| 作者单位： | 广西大学数学与信息科学学院,南宁,530004;南京航空航天大学民航学院,南京,210016;上海金融学院应用数学系,上海,201209 |
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| 基金项目： | 国家自然科学基金
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广西科学基金
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广西大学校科研和教改项目 |
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| 摘 要： | 1引言本文讨论带非线性互补约束的最优化问题: (MPEC) (?) (1)其中(x,y,w)∈R~(n m m),f∶R~(n m)→R,g=(g1,g2,…,gl)~T∶R~(n m)→R~l,F= (F_1,F_2…F_m)~T∶R~(n m)→R~m均是连续可微的,w⊥y表示向量w和y是正交的,即w~Ty=0,w ,y∈R~m．记(MPEC)可行集为X．这类问题广泛存在于工程技术、经济、博弈论等各个领域,有着直接的应用价值,故受到人们的广泛关注．关于这方面的应用及部分成果可参考文献1]-10]．显然,若将条件F(x,y)⊥y写成内积的形式F(x,y)~Ty=0,则(1)成为一个标准的光滑非线性规划问题(SSNP)．从理论上来说,现有的理论、方法和技术应可以解决问题(1)．遗憾的是,文献4]
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| 关 键 词： | 非线性互补 可行方向 约束规划 算法 广义 最优化问题 连续可微 MPEC |
| 修稿时间： | 2003-10-25 |
A GENERALIZED STRONGLY SUB-FEASIBLE ALGORITHM FOR MATHEMATICAL PROGRAMS WITH NONLINEAR COMPLEMENTARITY CONSTRAINTS |
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| Jian Jinbao,Qin Yi,Liang Yumei.A GENERALIZED STRONGLY SUB-FEASIBLE ALGORITHM FOR MATHEMATICAL PROGRAMS WITH NONLINEAR COMPLEMENTARITY CONSTRAINTS[J].Numerical Mathematics A Journal of Chinese Universities,2007,29(1):15-27. |
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| Authors: | Jian Jinbao Qin Yi Liang Yumei |
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| Institution: | College of Mathematics and Information Science, Guangxi University, Nanning 530004;College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016;Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209 |
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| Abstract: | This paper deals with discussion of a class of mathematical programs with nonlinear equibibrium constraints.At first,the problem is reformed as a gen- eral optimization problem by using a perturbed technique and a complememtarity function,then,combining the generalized projection technique and the idea of strongly subfeasible direction algorithm,a new algorithm for the discussed prob- lems is presented.Under suitable assumptions,the proposed algorithm is shown to possess global convergence and strong convergence.At last,some numerical results are reported. |
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| Keywords: | nonlinear complementarity constraints optimization generalized projection strongly subfeasible direction method convergence |
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