Studies on Development and Synthesis of Efficient Algorithms for Optimization and Equilibrium Problems

优化和平衡问题的高效算法的开发和综合研究

• 批准号: 08650079
• 负责人: FUKUSHIMA Masao
• 金额: $ 1.41万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08650079/
• 关键词: Optimization; Equilibrium Model; Algorithm; Variational Inequality Problem; Complementarity Problem

Variational inequality and complementarity problems are fundamental problems that are very useful in formulating various equilibrium problems arising not only in engineering such as transportation, structural mechanics and operations reseach but also in social sciences such as economics. In this project, we have conducted research on those fundamental equilibrium problems with particular emphasis on the optimization reformulation approach that have recently attracted much attention in this field. The main results which have been obtained during the last two years are summarized as follows :1.New approaches that reformulate variational inequality and complementarity problems as equivalent optimization problems have been proposed. Moreover novel algorithms that extend descent methods and Newton's method have been developed, and their effectiveness has been examined through extensive numerical experiments.2.New parallel and decomposition methods for variational inequality and complementarity problems have been developed by meking use of the idea of operator splitting and matrix splitting.3.New algorithms have been developed for solving mathematical program with equilibrium constraints for which a unified study has not been done so far.

变分的不平等和互补问题是基本问题，这些问题在制定各种平衡问题方面非常有用，不仅在工程学，结构力学和运营等工程中引起，而且在经济学等社会科学中也是如此。在这个项目中，我们对那些基本平衡问题进行了研究，特别强调了最近在该领域引起了很多关注的优化重新制作方法。在过去两年中获得的主要结果总结如下：1。新方法将变异不平等和互补性问题重新制定为等效优化问题。此外，已经开发了扩展下降方法和牛顿方法的新颖算法，并且已经通过广泛的数值实验来检查其有效性。2。New平行和分解方法用于变异不平等和互补性问题，已通过Mekke开发了用于对操作员启动和矩阵启动的概念的使用方案。到目前为止尚未完成统一的研究。

项目成果

M.Fukushima: "Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities" Complementarity and Variational Problems:State of the Art. (発表予定).

M.Fukushima：“互补性问题和变分不等式的评价函数的最小化和平稳序列”互补性和变分问题：最新技术（待提交）。

N.Yamashita and M.Fukushima: "Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems" Mathematical Programming. 76. 469-491 (1997)

N.Yamashita 和 M.Fukushima：“用于解决单调互补问题的半平滑重构的改进牛顿法”数学规划。

H.Jiang, M.Fukushima, L.Qi and D.Sun: "A trust region method for solving generalized complementarity problems" SIAM Journal on Optimization. (掲載予定).

H.Jiang、M.Fukushima、L.Qi 和 D.Sun：“解决广义互补问题的信任域方法”SIAM Journal on Optimization（即将出版）。

C.Kanzow: "Equivalence of the generalized complementarity problem to differentiable unconstrained minimization" J.Opt.Theory and Appl.90・3. 581-603 (1996)

C. Kanzow：“广义互补问题与可微无约束最小化的等价”J.Opt.Theory and Appl.90・3 (1996)。

N.Yamashita and M.Fukushima: "Equivalent unconstrained minimization and global error bounds for variational inequality problems" SIAM Journal on Control and Optimization. 35. 273-284 (1977)

N.Yamashita 和 M.Fukushima：“变分不等式问题的等效无约束最小化和全局误差界限”SIAM 控制与优化杂志。