Methods for Complementarity and Related Problems

互补性方法及相关问题

• 批准号: 22500256
• 负责人: FUKUSHIMA Masao
• 金额: $ 2.75万
• 依托单位: Nanzan University (2013)Kyoto University (2010-2012)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22500256/
• 关键词: 相補性; 最適化問題; 均衡問題; ゲーム理論; 変分不等式; 2次錐計画問題; 確率的相補性問題; 均衡制約付き最適化問題

Complementarity is one of the most fundamental concepts in mathematical optimization, which plays an essentially important role in the optimality conditions of optimization problems and the formulation of various equilibrium problems. In this study, we have developed practical methods with a solid theoretical basis, for complementarity and related problems including eigenvalue complementarity problems, optimization problems with second-order cone complementarity constraints, nonlinear second-order cone programming problems, Nash equilibrium problems, generalized Nash equilibrium problems, and multi-leader-follower games.

互补性是数学优化中最基本的概念之一，它在优化问题的最佳条件和各种均衡问题的制定中起着至关重要的作用。在这项研究中，我们开发了具有牢固理论基础的实用方法，用于互补性和相关问题，包括特征值互补性问题，二阶锥形互补性约束的优化问题，非线性二阶锥形编程问题，NASH平衡问题问题和多领导者游戏。

项目成果

Smoothing approach to Nash equilibrium formulations for a class of equilibrium problems with shared complementarity constraints

具有共享互补约束的一类均衡问题的纳什均衡公式的平滑方法

• DOI: 10.1007/s10589-011-9416-0
• 发表时间: 2012
• 期刊: Computational Optimization and Applications
• 影响因子: 2.2
• 作者: M. Hu;M. Fukushima
• 通讯作者: M. Fukushima

SOR- and Jacobi-type iterative methods for solving l_1-l_2 problems by way of Fenchel duality

通过 Fenchel 对偶性求解 l_1-l_2 问题的 SOR 和 Jacobi 型迭代方法

• DOI: 10.1007/s11590-011-0292-4
• 发表时间: 2012
• 期刊: Optimization Letters
• 影响因子: 1.6
• 作者: A. von Heusinger;C. Kanzow and M. Fukushima;M. Fukushima
• 通讯作者: M. Fukushima

Variational Inequality Formulation of a Class of Multi-Leader-Follower Games

• DOI: 10.1007/s10957-011-9901-8
• 发表时间: 2011-08
• 期刊: Journal of Optimization Theory and Applications
• 影响因子: 1.9
• 作者: Ming-shang Hu;M. Fukushima

Differentiable Exact Penalty Functions for Nonlinear Second-Order Cone Programs

• DOI: 10.1137/110852401
• 发表时间: 2012-12
• 期刊: SIAM J. Optim.
• 作者: E. H. Fukuda;Paulo J. S. Silva;M. Fukushima

Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets

• DOI: 10.1007/s10898-011-9719-9
• 发表时间: 2011-04
• 期刊: Journal of Global Optimization
• 影响因子: 1.8
• 作者: R. Nishimura;S. Hayashi;M. Fukushima