1997 Fiscal Year Annual Research Report

最適化・均衡問題に対する効率的アルゴリズムの構築と複合化に関する研究

Research Project

Project/Area Number	08650079
Research Institution	KYOTO UNIVERSITY
Principal Investigator	福嶋雅夫京都大学, 工学研究科, 教授 (30089114)
Co-Investigator(Kenkyū-buntansha)	山川栄樹高松大学, 経営学部, 講師 (20289333)
Keywords	最適化 / 均衡モデル / アルゴリズム / 変分不等式 / 相補性問題
Research Abstract	変分不等式問題およびそのサブクラスである相補性問題は,交通工学,構造力学,オペレーションズ・リサーチなどの工学諸分野だけでなく経済学等の社会科学においても頻繁に現れるさまざまな均衡問題を定式化する際に非常に有用な概念を提供する基本的な問題である.本研究においては,変分不等式・相補性問題のような均衡問題を最適化問題の枠組のもとに再構成するという,最近この分野で大きな注目を集めているアプローチに重点をおき,以下のような成果を得た. (1)変分不等式問題や相補性問題を最適化の枠組のもとに再構成する新しい方法を開発した.さらに,降下法やニュートン法等の反復法に基づく手法を拡張・複合化したアルゴリズムを構成し,その理論的性質を調べるとともに,計算機実験を通してその効率化を行った. (2)変分不等式問題や相補性問題に対して,作用素分割法や多重分割法などとの複合化による分解法および並列アルゴリズムの開発を行った. (3)実際の応用上非常に重要であるが,これまでほとんど体系的な研究が行なわれていなかった均衡条件を含む最適化問題に対する研究を行い,いくつかの新しい理論的結果を得るとともに,最適解を計算するための新しいアルゴリズムの開発を行った.

Research Products
(12 results)

All Other

All Publications (12 results)

[Publications] N.Yamashita and M.Fukushima: "Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems" Mathematical Programming. 76. 469-491 (1997)
[Publications] N.Yamashita and M.Fukushima: "Equivalent unconstrained minimization and global error bounds for variationainequality problems" SIAM Journal on Control and Optimization. 35. 273-284 (1997)
[Publications] M.Fukushima and J.-S.Pang: "Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities" Complementarity and Variational Problems : State of the Arts. 91-104 (1997)
[Publications] D.Sun, M.Fukushima and L.Qi.: "A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems" Complementarity and Variational Problems : State of the Arts. 452-472 (1997)
[Publications] N.Yamashita. K.Taji and M.Fukushima: "Unconstrained optimization reformulations of variational inequality problems" Journal of Optimization Theory and Applications. 92. 439-456 (1997)
[Publications] 山川栄樹, 牧英一, 福島雅夫: "分離可能な2次計画問題に対する非同期型ブロック並列アルゴリズム" システム制御情報学会論文誌. 10. 248-258 (1997)
[Publications] C.Kanzow, N.Yamashita and M.Fukushima: "New NCP-functions and their properties" Journal of Optimization Theory and Applications. 94. 115-135 (1997)
[Publications] 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).
[Publications] M.Fukushima and J.-S.Pang: "Some feasibility issues in mathematical programs with equilibrium constraints" SIAM Journal on Optimization. (掲載予定).
[Publications] M.Fukushima: "Parallel variable transformation in unconstrained optimization" SIAM Journal on Optimization. (掲載予定).
[Publications] M.Fukushima, Z.-Q. Luo and J.S.Pang: "A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints" Computational Optimization and Applications. (掲載予定).
[Publications] C.Kanzow and M.Fukushima: "Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities" Mathematical Programming. (掲載予定).

1997 Fiscal Year Annual Research Report

最適化・均衡問題に対する効率的アルゴリズムの構築と複合化に関する研究

Principal Investigator

福嶋 雅夫 京都大学, 工学研究科, 教授 (30089114)

Research Products

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

[Publications] N.Yamashita and M.Fukushima: "Equivalent unconstrained minimization and global error bounds for variationainequality problems" SIAM Journal on Control and Optimization. 35. 273-284 (1997)

[Publications] M.Fukushima and J.-S.Pang: "Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities" Complementarity and Variational Problems : State of the Arts. 91-104 (1997)

[Publications] D.Sun, M.Fukushima and L.Qi.: "A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems" Complementarity and Variational Problems : State of the Arts. 452-472 (1997)

[Publications] N.Yamashita. K.Taji and M.Fukushima: "Unconstrained optimization reformulations of variational inequality problems" Journal of Optimization Theory and Applications. 92. 439-456 (1997)

[Publications] 山川栄樹, 牧英一, 福島雅夫: "分離可能な2次計画問題に対する非同期型ブロック並列アルゴリズム" システム制御情報学会論文誌. 10. 248-258 (1997)

[Publications] C.Kanzow, N.Yamashita and M.Fukushima: "New NCP-functions and their properties" Journal of Optimization Theory and Applications. 94. 115-135 (1997)

[Publications] 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).

[Publications] M.Fukushima and J.-S.Pang: "Some feasibility issues in mathematical programs with equilibrium constraints" SIAM Journal on Optimization. (掲載予定).

[Publications] M.Fukushima: "Parallel variable transformation in unconstrained optimization" SIAM Journal on Optimization. (掲載予定).

[Publications] M.Fukushima, Z.-Q. Luo and J.S.Pang: "A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints" Computational Optimization and Applications. (掲載予定).

[Publications] C.Kanzow and M.Fukushima: "Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities" Mathematical Programming. (掲載予定).

福嶋雅夫京都大学, 工学研究科, 教授 (30089114)