大規模非線形最適化問題に対する内点法の研究

大规模非线性优化问题的内点法研究

• 批准号: 05740151
• 负责人: 土谷 隆
• 金额: $ 0.32万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Encouragement of Young Scientists (A)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-05740151/
• 关键词: 内点法; アフィンスケーリング法; 大域的収束性

数理計画問題に対する内点法の研究を行い,得られた成果を次の2つの論文にまとめた。(1)制約条件を満たさないような初期内点から出発するアフィンスケーリング法の拡張について。(M.Muramatsu and T.Tsuchiya:An Affine Scaling Algorithm with an Infeasible Starting Point.Research Memorandum No.490,The Institute of Statistical Mathematics,January,1994.(Annals of Operations Researchに投稿中。))(2)狭義2次計画問題に対するアフィンスケーリング法の大域的収束性。(T.Tsuchiya:Global Convergence of the Affine Scaling Algorithm for Strictly Convex Quadratic Programming Problems.(投稿準備中。))研究代表者は,著名な内点法である線形計画問題に対するアフィンスケーリング法に対して局所的に定義されたポテンシャル関数を用いた解析を考案し,その大域的収束性に関し現在までで最良の理論的結果を得てきた。(1),(2)は,その延長上にある研究である。(1)は,線形計画問題に対するアフィンスケーリング法を制約領域の外部から制約条件を満たしつつ最適解に近づいていく“非実行可能内点法"に拡張したものである。(2)は,一番単純な非線形計画問題である狭義凸2次計画問題に対するアフィンスケーリング法の大域的収束性を証明したものである。これらの結果を,1993年5月のアメリカOR学会大会で発表した。

The mathematical drawing problem has been studied by the interior point method, and the results have been obtained for two times. (1) the conditions of the agreement are as follows: (1) the conditions of the agreement are as follows: (1) the conditions of the agreement are as follows: (1) the conditions of the agreement are as follows: (1) the conditions of the agreement are as follows: (1) the conditions of the agreement are as follows: (1) the conditions of the agreement are as follows: (1) the conditions of the agreement are as follows: (1) the conditions of the agreement. (M.Muramatsu and T.Tsuchiya:An Affine Scaling Algorithm with an Infeasible Starting Point.Research Memorandum No.490,The Institute of Statistical Mathematics,January,1994. (Annals of Operations Research submission.)) (2) in a narrow sense, the two-time planning of the problem is related to the limitation of the method. (T.Tsuchiya:Global Convergence of the Affine Scaling Algorithm for Strictly Convex Quadratic Programming Problems. (preparation for submission.)) The representative of the research, the well-known interior point method, the shape design problem, the interior point method, the well-known interior point method, the interior point method, the (1), (2) to extend the level of research and development. (1) the problem of shape planning is the most effective way to solve the problem of non-linear planning in the field. (2) on the basis of the information on the non-linear drawing problem, the narrow convex of the problem twice, the problem area of the general area of the non-linear drawing problem, the narrow convex twice, the problem problem, the problem and the problem. The results of the meeting of the OR Society were reviewed in May 1993.

项目成果

O.Guler,T.Tsuchiya 他: "Degeneracy in Interior Point Methods for Linear Programming:a Survey" Annals of Operations Research. 46. 107-138 (1993)

O.Guler、T.Tsuchiya 等人：“线性规划内点方法的简并性：一项调查”运筹学年鉴 46. 107-138 (1993)。

M.G.C.Resende,T.Tsuchiya 他: "Identifying the Optimal Face of a Network Linear Program with a Globally Convergent Interior Point Method" Large Scale Optimization:State of the Art(Kluwer Academic Publishes). 371-396 (1994)

M.G.C.Resende、T.Tsuchiya 等人：“使用全局收敛内点方法识别网络线性规划的最优面”大规模优化：最新技术（Kluwer 学术出版）371-396 (1994)。

Takashi Tsuchiya: "Global Convergence of the Affine Scaling Algorithms for the Primal Degenerate Strictly Convex Quadratic Programming Problems" Annals of Operations Research. 47. 509-539 (1991)

Takashi Tsuchiya：“原始退化严格凸二次规划问题的仿射缩放算法的全局收敛”运筹学年鉴。

R.D.C.Monteiro,T.Tsuchiya 他: "A Simplified Global Convergence Proof of the Affine Scaling Algorithm" Annals of Operations Research. 47. 443-482 (1993)

R.D.C.Monteiro、T.Tsuchiya 等人：“仿射缩放算法的简化全局收敛证明”运筹学年鉴 47. 443-482 (1993)。