共查询到10条相似文献,搜索用时 78 毫秒
1.
Suhel Ahmad Khan 《Journal of Global Optimization》2011,49(4):695-705
In this paper, we introduce and study a generalized class of vector implicit quasi complementarity problem and the corresponding
vector implicit quasi variational inequality problem. By using Fan-KKM theorem, we derive existence of solutions of generalized
vector implicit quasi variational inequalities without any monotonicity assumption and establish the equivalence between those
problems in Banach spaces. 相似文献
2.
Muhammad Aslam Noor 《Journal of Applied Mathematics and Computing》2003,11(1-2):165-172
In this paper, we introduce the concept of well-posedness for general variational inequalities and obtain some results under pseudomonotonicity. It is well known that monotonicity implies pseudomonotonicity, but the converse is not true. In this respect, our results represent an improvement and refinement of the previous known results. Since the general variational inequalities include (quasi) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. 相似文献
3.
Lili Huan Biao Qu Jin-guang Jiang 《Journal of Applied Mathematics and Computing》2010,33(1-2):411-421
In this paper, we present some merit functions for general mixed quasi-variational inequalities, and we obtain the equivalent optimization problems to general mixed quasi-variational inequalities. Since the general mixed quasi-variational inequalities include general variational inequalities, quasi-variational inequalities and nonlinear (implicit) complementarity problems as special cases, our results continue to hold for these problems. In this respect, results obtained in this paper represent an extension of previously known results. 相似文献
4.
In this paper we introduce and study a number of new classes of quasi variational inequalities. Using essentially the projection technique and its variant forms we prove that the generalized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations (normal maps). This equivalence enables us to suggest a number of iterative algorithms for solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational inequalities, we obtain a class of quasi variational inequalities studied by Siddiqi, Husain and Kazmi [35], but there are several inaccuracies in their formulation of the problem, the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of their results can be obtained as special cases from our main results. 相似文献
5.
6.
MUHAMMAD ASLAM NOOR 《Journal of Global Optimization》2000,18(1):75-89
In this paper, we suggest and analyze a number of resolvent-splitting algorithms for solving general mixed variational inequalities by using the updating technique of the solution. The convergence of these new methods requires either monotonicity or pseudomonotonicity of the operator. Proof of convergence is very simple. Our new methods differ from the existing splitting methods for solving variational inequalities and complementarity problems. The new results are versatile and are easy to implement. 相似文献
7.
《Journal of Computational and Applied Mathematics》2001,135(1):111-124
In this paper, we suggest and analyze a number of four-step resolvent splitting algorithms for solving general mixed variational inequalities by using the updating technique of the solution. The convergence of these new methods requires either monotonicity or pseudomonotonicity of the operator. Proof of convergence is very simple. Our new methods differ from the existing splitting methods for solving variational inequalities and complementarity problems. The new results are versatile and are easy to implement. 相似文献
8.
Merit functions for general variational inequalities 总被引:1,自引:0,他引:1
Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2006,316(2):736-752
In this paper, we consider some classes of merit functions for general variational inequalities. Using these functions, we obtain error bounds for the solution of general variational inequalities under some mild conditions. Since the general variational inequalities include variational inequalities, quasivariational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. In this respect, results obtained in this paper represent a refinement of previously known results for classical variational inequalities. 相似文献
9.
M. A. Noor 《分析论及其应用》1996,12(3):18-28
In this paper, we introduce and study a new class of quasi variational inequalities. Using essentially the projection technique
and its variant forms, we establish the equivalence between generalized nonlinear quasi variational inequalities and the fixed
point problems. This equivalence is then used to suggest and analyze a number of new iterative algorithms. These new results
include the corresponding known results for generalized quasi variational inequalities as special cases. 相似文献
10.
G. Isac 《Journal of Global Optimization》2005,31(3):405-420
In several recent papers we obtained existence theorems for complementarity problems and variational inequalities using for each of them a particular notion of exceptional family of elements. Now, in this paper we introduce a new notion of exceptional family of elements. This notion is based on an Implicit Leray-Schauder Alternative. By this new notion we obtain a unification of the study of solvability of complementarity problems and of variational inequalities. The paper is finished with a section dedicated to variational inequalities with δ-pseudomonotone operators. 相似文献