1999 Fiscal Year Annual Research Report

微分不可能な方程式に対する平滑化ニュートン法

Research Project

Project/Area Number	11640119
Research Institution	Shimane University
Principal Investigator	陳小君島根大学, 総合理工学部, 助教授 (70304251)
Co-Investigator(Kenkyū-buntansha)	福島雅夫京都大学, 情報学研究科, 教授 (30089114) 山本哲朗愛媛大学, 理学部, 教授 (80034560) 山崎稀嗣島根大学, 総合理工学部, 教授 (70032935) 杉江実郎島根大学, 総合理工学部, 教授 (40196720) 古用哲夫島根大学, 総合理工学部, 教授 (40039128)
Keywords	微分不可能 / 方程式 / 平滑化 / ニュートン法
Research Abstract	研究代表者は1999年4月から2000年3月まで従来の研究の自然な延長として研究課題"微分不可能な方程式に対する平滑化ニュートン法"につき研究し、5篇の論文を国際誌に共同で発表した。また、6篇の論文を国際誌に単独および共同で発表する予定になっている(掲載受理済)。主要な成果は次のようである。 1.島根大学山崎教授(本研究分担者)とともに、線形補償問題を微分不可能な方程式に書き直し、それを用いて与えられた問題が解をもつか否かを検証する方法を提案した。 2.愛媛大学山本教授(本研究分担者)とともに、微分不可能なDirichlet問題を解くNewton型解法の収束を証明した。 3.京都大学福島教授(本研究分担者)とともに、微分不可能な凸最適化問題を解くQuasi-Newton型解法の収束を証明した。 4.Karlsruhe大学Alefeld教授,Maryland大学Potra教授,Iowa大学Ye教授,Washington Sate大学Chen教授,New South Wales大学Womesley博士, Hamburg大学Kanzow教授とともに微分不可能な方程式に関する研究を行った。

Research Products
(11 results)

All Other

All Publications (11 results)

[Publications] X. Chen, M. Fukushima: "Proximal quasi-Newton methods for nondifferentiable convex optimization"Mathematical Programming. 85. 313-334 (1999)
[Publications] G.E.Alefeld, X. Chen, F.A. Potra: "Numerical validation of solutions of linear complementarity problems"Numerische Mathematik. 83. 1-23 (1999)
[Publications] X. Chen, Y. Ye: "On homotopy-smoothing methods for box-constrained variational inequlities"SIAM J. Control and Optimization. 37. 589-616 (1999)
[Publications] B. Chen, X. Chen, C. Kanzow: "A penalizaed Fischer-Burmeister NCP-function"Mathematical Programming. (to appear).
[Publications] X. Chen., Y. Shogenji, M. Yamasaki: "Verification for existence of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear).
[Publications] X. Chen, R. Womersley: "Randon test problems and parallel methods quadratic programs and quadratic stochastic program"Optimization Methods and Softwares. (to appear).
[Publications] B. Chen, X. Chen: "A global local superlinear contimuation-smoothing method for Po and Ro or monotone NCP"SIAM J. Optimization. 9. 624-645 (1999)
[Publications] X. Chen, N.Matsunaga, T. Yamamoto: "Smoothing Newton methods for nonsmooth Dirichelet problems"in: M. Fukushima and L. Qi, Eds., Kluwer Academic Pub.. 65-79 (1999)
[Publications] X. Chen: "Smoothing methods for complementarity problems and their applications: a survey"Journal of the Operations Research Society of Japan. (to appear).
[Publications] X. Chen: "Newton-type methods for stochastic programming,"Mathematical and Computer Modelling. (to appear).
[Publications] B. Chen, X. Chen: "A global linear and local quadratic continuation smoothing method for variational inequalities"Computational Optimization and Applications. (to appear).

1999 Fiscal Year Annual Research Report

微分不可能な方程式に対する平滑化ニュートン法

Principal Investigator

陳 小君 島根大学, 総合理工学部, 助教授 (70304251)

Research Products

[Publications] X. Chen, M. Fukushima: "Proximal quasi-Newton methods for nondifferentiable convex optimization"Mathematical Programming. 85. 313-334 (1999)

[Publications] G.E.Alefeld, X. Chen, F.A. Potra: "Numerical validation of solutions of linear complementarity problems"Numerische Mathematik. 83. 1-23 (1999)

[Publications] X. Chen, Y. Ye: "On homotopy-smoothing methods for box-constrained variational inequlities"SIAM J. Control and Optimization. 37. 589-616 (1999)

[Publications] B. Chen, X. Chen, C. Kanzow: "A penalizaed Fischer-Burmeister NCP-function"Mathematical Programming. (to appear).

[Publications] X. Chen., Y. Shogenji, M. Yamasaki: "Verification for existence of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear).

[Publications] X. Chen, R. Womersley: "Randon test problems and parallel methods quadratic programs and quadratic stochastic program"Optimization Methods and Softwares. (to appear).

[Publications] B. Chen, X. Chen: "A global local superlinear contimuation-smoothing method for Po and Ro or monotone NCP"SIAM J. Optimization. 9. 624-645 (1999)

[Publications] X. Chen, N.Matsunaga, T. Yamamoto: "Smoothing Newton methods for nonsmooth Dirichelet problems"in: M. Fukushima and L. Qi, Eds., Kluwer Academic Pub.. 65-79 (1999)

[Publications] X. Chen: "Smoothing methods for complementarity problems and their applications: a survey"Journal of the Operations Research Society of Japan. (to appear).

[Publications] X. Chen: "Newton-type methods for stochastic programming,"Mathematical and Computer Modelling. (to appear).

[Publications] B. Chen, X. Chen: "A global linear and local quadratic continuation smoothing method for variational inequalities"Computational Optimization and Applications. (to appear).

陳小君島根大学, 総合理工学部, 助教授 (70304251)