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Construction of theory of polyhedral approximation of the semi-definite cone in conic optimization and its applications

二次曲线优化中半定锥多面体逼近理论的构建及其应用

基本信息

批准号：
19H02373
负责人：
吉瀬章子
金额：
$ 10.98万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2019
资助国家：
日本
起止时间：
2019-04-01 至 2023-03-31
项目状态：
已结题

项目摘要

錐最適化モデルは，線形計画問題や半正定値計画問題を含む広範な最適化モデルであり，21世紀を代表する最適化モデルとして世界的規模で活発に研究が行われている．本研究では，2次割当問題など困難な数理最適化問題に対する「錐最適化モデル」の高い問題記述能力に着目し，応募者らが発案した半正定値基とそれらの拡張によって生成される多様な凸多面錐を精査することで，錐最適化手法のさらなる社会実装に役立つ，半正定値錐の凸多面錐近似の理論を構築することを目的としている．理論的性質の導出と計算機実験を繰り返すことにより，計算効率と近似精度の双方から半正定値錐の凸多面錐近似の限界を見極め，半正定値錐の凸多面錐近似に関する独自の理論を構築するとともに，錐最適化の社会実装を意識した，計算効率の議論と検証を重視した理論構築を目指している．2021年度は，特に小さなサイズの主座小行列式が非負である性質をもつ行列錐に着目し，半正定値錐の凸多面錐近似における近似精度の導出を試みるととともに，0-1整数計画問題あるいは混合整数計画問題への応用可能性を検証するため，0-1制約の連続緩和による線形計画問題を子問題とする従来手法と，連続緩和の代わりに半正定値緩和の凸多面錐近似を用いた手法の比較を行った．研究代表者吉瀬は理論の構築，応用可能性の検証など研究全般にわたる役割を担った．研究分担者の繁野氏には組合せ最適化に関する専門知識を，八森氏には組合せ論に関する専門知識を，高野氏には混合整数計画問題や大域的最適化に関する専門知識を，佐野氏には離散数学に関する専門知識を，それぞれご提供頂いた．

In this study, the problem of mathematical optimization, mathematical optimization. In the case of a fund-raiser, there is a case in which a semi-definite foundation is used to generate information about how to generate a multi-function, a convex multi-faceted device, a multi-faceted tool, a social tool, a social device, a semi-definite tool, a convex model, a theory, a computer, and a computer. Calculate the accuracy of rate approximation, positive semidefinite approximation, convex polyhedral approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedral approximation, positive semidefinite approximation, convex polyhedr In particular, the small determinant of the principal seat is characterized by the number of non-linear determinants, the positive semidefinite order, the convex polyhedral approximation, the approximate accuracy, the 0-1 integer drawing problem, the mixed integer drawing problem, the possibility, the possibility, the accuracy, the possibility, the possibility, the accuracy, the accuracy, the possibility, the possibility, the accuracy, the accuracy, the possibility, the accuracy, the possibility, the possibility, the accuracy, the accuracy, the possibility, the possibility, the accuracy, the accuracy, the possibility, the possibility, the accuracy, the accuracy, the possibility, the possibility, the accuracy, the possibility, the accuracy, In the 0-1 system, the sub-problems of the link and shape planning problems are divided into two parts: the semi-definite method and the convex polyhedral approximation. the representative of the research is to compare the theory and theory. In this paper, we use the possibility method to study the whole range of knowledge. The research contributor Feno organized the most advanced knowledge, Hassen organized the knowledge, Takano mixed integer drawing problem knowledge, Sano spread mathematical knowledge, and Takano provided information.