自反Banach空间内混合非线性似变分不等式解的算法<sup>*</sup>

丁协平

自反Banach空间内混合非线性似变分不等式解的算法^*

丁协平

四川师范大学数学系, 成都 610066

基金项目: * 国家自然科学基金资助项目(19371058)

详细信息

中图分类号: O177;O176
计量
- 文章访问数: 2281
- HTML全文浏览量: 170
- PDF下载量: 767
- 被引次数: 0
出版历程
- 收稿日期: 1996-09-09
- 刊出日期: 1998-06-15

Algorithm of Solutions for Mixed Nonlinear Variational-Like Inequalities in Reflexive Banach Space

Ding Xieping

Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China

摘要

摘要: 本文在自反Banach空间内研究了一类混合非线性似变分不等式应用作者得到的一个极小极大不等式,对这类混合非线性似变分不等式的解,证明了几个存在唯一性定理其次由应用辅助问题技巧,作者建议了一个计算此类混合非线性似变分不等式的近似解的创新算法最后讨论收敛性准则.
- 混合非线性似变分不等式 /
- 极小极大不等式 /
- 辅助变分不等式 /
- 一般算法 /
- 自反Banach空间
Abstract: In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequalit y obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, the author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.
- mixed nonlinear variational-like inequality /
- minimax inequality /
- auxiliary variational inequality /
- general algorithm /
- reflexive Banach space

HTML全文

参考文献(16)

[1]	M.A.Noor,Nonconvex functions and variational inequalities,J.Optim.Theory Appl.,87(3)(1995),615-630.
[2]	J.Parida,M.Sahoo and A.Kumar,A variational-like inequality problem,Bull.Austral.Math.Soc.,39(1989),225-231.
[3]	N.H.Dien,Some remarks on variational-like and quasivariational-like inequalities,Bull.Austral.Math.Soc.,46(1992),335-342.
[4]	J.C.Yao,Existence of generalized variational inequalities,Opera.Research Lett.,15(1994),35-40.
[5]	X.P.Ding,General algorithm of solutions for nonlinear variational inequalities in Banach spaces,Internat.J.Computers Math.Appl.,34(9)(1997),131-137.
[6]	P.T.Harker and J.S.Pang,Finite-dimensional variational inequality and nonlinear complementarity problems:A survey of theory,algorithms and applications,Math.Programming.Ser.B.,48(1990),161-221.
[7]	G.Isac,Complementarity problems,Lecture Notes in Mathematics,1528,Springer,Berlin(1992),16-50.
[8]	M.A.Noor,General variational inequalities,Appl.Math.Lett.,1(2)(1988),119-122.
[9]	M.A.Noor,Mixed variational inequalities,Appl.Math.Lett.,3(2)(1990),73-75.
[10]	M.A.Noor,General algorithm for variational inequalities,J.Optim.Theory.Appl.,73(2)(1992),409-413.
[11]	M.A.Noor,K.I.Noor and T.M.Rassias,Some aspects of variational inequalities,J.Comput.Appl.Math.,47(1993),285-312.
[12]	X.P.Ding and E.Tarafdar,Existence and uniqueness of solutions for a general nonlinear variational inequality,Appl.Math.Lett.,8(1)(1995),31-36.
[13]	J.X.Zhou and G.Chen,Diagonal convexity conditions for problems in convex analysis and quasi variational inequalities,J.Math.Anal.Appl.,132(1988),213-225.
[14]	X.P.Ding and K.K.Tan,A minimax inequality with applications to existence of equilibrium point and fixed point theorems,Colloquium Math.,63(2)(1992),233-247.
[15]	I.Ekeland and R.Temam,Convex Analysis and Variational Problems,North-Holland,Amsterdam,Holland(1976).
[16]	G.Cohen,Auxiliary problem principle extend to variational inequalities,J.Optim.Theory Appl.,59(2)(1988),325-333.