Application of conic constrained semi-infinite programming to filter design and DSM communication

圆锥约束半无限规划在滤波器设计和DSM通信中的应用

• 批准号: 22760064
• 负责人: HAYASHI Shunsuke
• 金额: $ 2.66万
• 依托单位: Tohoku University (2013)Kyoto University (2010-2012)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 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-22760064/
• 关键词: 数理工学; 最適化; 半無限計画; 錐計画; フィルタ設計; 国際研究者交流（台湾）

When I first applied for this fund, the purposes of the study are to establish an efficient algorithm for semi-infinite programming problems with conic constraints, and to apply the established algorithm to real problems such as filter design, DSM communication and so on. On establishing the algorithms, we have accomplished the first purpose sufficiently. Especially, the most remarkable result is to have proposed the regularized explicit exchange method for semi-infinite conic programming problems, which was accepted for publication in SIAM Journal on Optimization. On the other hand, concerning the real application, we could not obtain sufficient results on the DSM communication. However, we applied the regularized explicit exchange method to the vector Chebyshev approximation problem, which includes the FIR filter design problems as a subclass.

当我第一次申请这个基金的时候，研究的目的是建立一种针对二次曲线约束的半无限规划问题的高效算法，并将所建立的算法应用到滤波器设计、DSM通信等实际​​问题中。在算法的建立上，我们已经充分实现了第一个目的。其中最引人注目的成果是提出了半无限二次曲线规划问题的正则化显式交换方法，并被SIAM Journal on Optimization接受发表。另一方面，就实际应用而言，我们在DSM通信上无法获得足够的结果。然而，我们将正则化显式交换方法应用于向量切比雪夫近似问题，其中包括作为子类的 FIR 滤波器设计问题。

项目成果

Equilibrium problems related to conic complementarity problems

与圆锥曲线互补问题相关的平衡问题

• 发表时间: 2013
• 作者: Shunsuke Hayashi

A smoothing SQP method for mathematical programs with second-order cone complementarity constraints

具有二阶锥互补约束的数学规划的平滑SQP方法

• 发表时间: 2012
• 作者: Hiroshi Yamamura; Takayuki Okuno; Shunsuke Hayashi;Masao Fukushima
• 通讯作者: Masao Fukushima

Semidefinite complementarity reformulation for robust Nash equilibrium problems based on the duality of nonconvex quadratic programming

基于非凸二次规划对偶性的稳健纳什均衡问题的半定互补重构

• 发表时间: 2010
• 作者: Ryoichi Nishimura; Shunsuke Hayashi;Masao Fukushima
• 通讯作者: Masao Fukushima

Robust Nash equilibria in incomplete information games : semidefinite complementarity reformulation and equilibrium behavior

不完全信息博弈中的鲁棒纳什均衡：半定互补重构和均衡行为

• 发表时间: 2010
• 作者: Ryoichi Nishimura; Shunsuke Hayashi;Masao Fukushima
• 通讯作者: Masao Fukushima

Robust optimization equilibrium and conic complementarity problems

鲁棒优化平衡和二次曲线互补问题

• 作者: Shunsuke Hayashi