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研究生:李子安
研究生(外文):Zhi-an Lee
論文名稱:近似變分不等式解之穩定性
論文名稱(外文):On the solution stability of quasivariational inequality
指導教授:王牧民黃毅青
指導教授(外文):Mu-Ming WongNgai-Ching Wong
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:22
中文關鍵詞:下半連續參數變分不等式度量投影近似變分不等式維度定理
外文關鍵詞:lower semi-continuitydegree theoryparametric variational inequalitymetric projectionquasi-variational inequality
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我們將討論非單調算子的參數近似變分不等式解之穩定性,藉由維度定理和自然映射顯示出這問題的解映射在某些條件下是下半連續。
We will study the solution stability of a parametric quasi-variational inequality without the monotonicity assumption of operators. By using the degree theory and the natural map we show that under certain conditions, the solution map of the problem is lower semi-continuous with respect to parameters.
1. INTRODUCTION
2. MAIN RESULTS
3. REFERENCE
1. S. Adly, M. A. Mansour and L. Scrimali, Stability and sensitivity analysis of elastic traffic network problems and quasivariational inequalities,Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 3(2005),767-771.
2. L. Ambrosio and N. Dancer, Calculus of variations and partial differential equations : topics on geometrical evolution problems and degree theory, Springer, 2000, Berlin.
3. Claudio Baiocchi and Antonio Capelo, Variational and Quasivariational Inequalities, Wiley, 1984, Chichester West Sussex.
4. S. Dafermos, Sensitivity analysis in variational inequalities, Math.Oper. Res. 13(1988), 421-434.
5. A. Domokos, Solution sensitivity of variational inequalities, J. Math.Math. Appl. 230(1999), 382-389.
6. B. T. Kien and M. M. Wong, On the solution stability of variational inequalities, J. Global Optim. 39(2007), no.1, 101-111.
7. A. B. Levy and R.T. Rockafellar, Sensitivity analysis of solutions to generalized equations, Transactions of the American Mathematical Society, 345(1994), 661-671.
8. James R. Munkres, Topology: a first course, Prentice-Hall, 1975,Englewood Cliffs N.J.
9. Donal O’Regan, Yeol Je Cho, and Yu-Qing Chen, Topological Degree Theory and Applications, Chapman and Hall/CRC, 2006, Boca Raton FL.
10. R. T. Rockafellar, Proto-differentiability of set-valued mappings and its applications in optimization, Annales de I’Institut H. Poincare; Analyse Non Lineaire 6(1989), 449-482.
11. Hwai-Chiuan Wang, Nonlinear Analysis, National Tsing Hua University Press (Taiwan), 2003, Hsinchu Taiwan.
12. N. D. Yen, H¨older continuity of solution to a parametric variational inequality, Appl. Math. Optim, 31(1995) 245-255.
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