共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we introduce and consider a new class of mixed variational inequalities, which is called the general mixed
variational inequality. Using the resolvent operator technique, we establish the equivalence between the general mixed variational
inequalities and the fixed-point problems as well as resolvent equations. We use this alternative equivalent formulation to
suggest and analyze some iterative methods for solving the general mixed variational inequalities. We study the convergence
criteria of the suggested iterative methods under suitable conditions. Using the resolvent operator technique, we also consider
the resolvent dynamical systems associated with the general mixed variational inequalities. We show that the trajectory of
the dynamical system converges globally exponentially to the unique solution of the general mixed variational inequalities.
Our methods of proofs are very simple as compared with others’ techniques. Results proved in this paper may be viewed as a
refinement and important generalizations of the previous known results. 相似文献
2.
Muhammad Aslam Noor 《Journal of Applied Mathematics and Computing》2010,32(1):83-95
In this paper, we introduce and study a new class of variational inequalities involving three operators, which is called the extended general variational inequality. Using the projection technique, we show that the extended general variational inequalities are equivalent to the fixed point and the extended general Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze a number of projection iterative methods for solving the extended general variational inequalities. We also consider the convergence of these new methods under some suitable conditions. Since the extended general variational inequalities include general variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems. 相似文献
3.
Muhammad Aslam Noor 《Computational Mathematics and Modeling》2010,21(1):97-108
It is well known that the nonconvex variational inequalities are equivalent to the fixed point problems. We use this equivalent
alternative formulation to suggest and analyze a new class of two-step iterative methods for solving the nonconvex variational
inequalities. We discuss the convergence of the iterative method under suitable conditions. We also introduce a new class
of Wiener – Hopf equations. We establish the equivalence between the nonconvex variational inequalities and the Wiener – Hopf
equations. This alternative equivalent formulation is used to suggest some iterative methods. We also consider the convergence
analysis of these iterative methods. Our method of proofs is very simple compared to other techniques. 相似文献
4.
In this paper, we introduce and study a new class of extended general nonlinear mixed variational inequalities and a new class of extended general resolvent equations and establish the equivalence between the extended general nonlinear mixed variational inequalities and implicit fixed point problems as well as the extended general resolvent equations. Then by using this equivalent formulation, we discuss the existence and uniqueness of solution of the problem of extended general nonlinear mixed variational inequalities. Applying the aforesaid equivalent alternative formulation and a nearly uniformly Lipschitzian mapping S, we construct some new resolvent iterative algorithms for finding an element of set of the fixed points of nearly uniformly Lipschitzian mapping S which is the unique solution of the problem of extended general nonlinear mixed variational inequalities. We study convergence analysis of the suggested iterative schemes under some suitable conditions. We also suggest and analyze a class of extended general resolvent dynamical systems associated with the extended general nonlinear mixed variational inequalities and show that the trajectory of the solution of the extended general resolvent dynamical system converges globally exponentially to the unique solution of the extended general nonlinear mixed variational inequalities. The results presented in this paper extend and improve some known results in the literature. 相似文献
5.
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
6.
《Journal of Mathematical Analysis and Applications》1987,128(1):138-155
In this paper, we introduce and study a new unified and general class of variational inequalities. We derive the general error estimates for the finite element solutions of variational inequalities. It has been shown that a class of contact problems with friction terms arising in elastostatics can be studied in the framework of variational inequalities. Several special cases, which can be obtained from the general results, are also discussed. 相似文献
7.
In this paper, we introduce and study a class of differential vector variational inequalities in finite dimensional Euclidean spaces. We establish a relationship between differential vector variational inequalities and differential scalar variational inequalities. Under various conditions, we obtain the existence and linear growth of solutions to the scalar variational inequalities. In particular we prove existence theorems for Carathéodory weak solutions of the differential vector variational inequalities. Furthermore, we give a convergence result on Euler time-dependent procedure for solving the initial-value differential vector variational inequalities. 相似文献
8.
S. I. Repin 《Journal of Mathematical Sciences》2009,157(6):874-884
A new method for obtaining computable estimates for the difference between exact solutions of elliptic variational inequalities
and arbitrary functions in the respective energy space is suggested. The estimates are obtained by transforming the corresponding
variational inequality without the use of variational duality arguments. These estimates are valid for any function in the
energy class and contain no constants depending on the mesh used to find an approximate solution. This method for linear elliptic
and parabolic problems was earlier suggested by the author. The guaranteed error bounds we derive can be of two types. Estimates
of the first type contain only one global constant, which is a constant in the Friedrichs type inequality. Estimates of the
second type are based on the decomposition of Ω into convex subdomains and the Payne–Weinberger inequalities for these subdomains.
Bibliography: 20 titles.
Translated from Problems in Mathematical Analysis
39 February, 2009, pp. 81–90. 相似文献
9.
A Logarithmic-Quadratic Proximal Prediction-Correction Method for Structured Monotone Variational Inequalities 总被引:1,自引:0,他引:1
Inspired by the Logarithmic-Quadratic Proximal (LQP) method for variational inequalities, we present a prediction-correction
method for structured monotone variational inequalities. Each iteration of the new method consists of a prediction and a correction.
Both the predictor and the corrector are obtained easily with tiny computational load. In particular, the LQP system that
appears in the prediction is approximately solved under significantly relaxed inexactness restriction. Global convergence
of the new method is proved under mild assumptions. In addition, we present a self-adaptive version of the new method that
leads to easier implementations. Preliminary numerical experiments for traffic equilibrium problems indicate that the new
method is effectively applicable in practice.
Presented at the 6th International conference on Optimization: Techniques and Applications, Ballarat Australia, December 9–11,
2004.
This author was supported by NSFC Grant 10571083, the MOEC grant 20020284027 and Jiangsu NSF grant BK2002075 相似文献
10.
S. I. Repin 《Journal of Mathematical Sciences》2008,152(5):702-712
The paper is concerned with a new way of deriving computable estimates for the difference between the exact solutions of elliptic
variational inequalities and arbitrary functions in the corresponding energy space that satisfy the main (Dirichlét) boundary
conditions. Unlike the method derived earlier, the estimates are obtained by certain transformations of variational inequalities
without using duality arguments. For linear elliptic and parabolic problems, this method was suggested by the author in previous
papers. The present paper deals with two different types of variational inequalities (also called variational inequalities
of the first and second kind). The techniques discussed can be applied to other nonlinear problems related to variational
inequalities. Bibliography: 20 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 147–164. 相似文献
11.
Muhammad Aslam Noor Khalida Inayat Noor Th.M Rassias 《Journal of Mathematical Analysis and Applications》1998,220(2):804
In this paper, we introduce and study a new class of variational inequalities, which is called the generalized set-valued mixed variational inequality. The resolvent operator technique is used to establish the equivalence among generalized set-valued variational inequalities, fixed point problems, and the generalized set-valued resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area. 相似文献
12.
Joachim Gwinner 《Optimization》2017,66(8):1323-1336
AbstractThis paper addresses a class of inequality constrained variational inequalities and nonsmooth unilateral variational problems. We present mixed formulations arising from Lagrange multipliers. First we treat in a reflexive Banach space setting the canonical case of a variational inequality that has as essential ingredients a bilinear form and a non-differentiable sublinear, hence convex functional and linear inequality constraints defined by a convex cone. We extend the famous Brezzi splitting theorem that originally covers saddle point problems with equality constraints, only, to these nonsmooth problems and obtain independent Lagrange multipliers in the subdifferential of the convex functional and in the ordering cone of the inequality constraints. For illustration of the theory we provide and investigate an example of a scalar nonsmooth boundary value problem that models frictional unilateral contact problems in linear elastostatics. Finally we discuss how this approach to mixed formulations can be further extended to variational problems with nonlinear operators and equilibrium problems, and moreover, to hemivariational inequalities. 相似文献
13.
14.
《Mathematical and Computer Modelling》1999,29(5):1-11
In this paper, we introduce and study a new class of variational inequalities, which is called the set-valued mixed quasi-variational inequality. The resolvent operator technique is used to establish the equivalence among generalized set-valued mixed quasi-variational inequalities, fixed-point problems and the set-valued implicit resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area. 相似文献
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17.
A class of matrix optimization problems can be formulated as a linear variational inequalities with special structures. For solving such problems, the projection and contraction method (PC method) is extended to variational inequalities with matrix variables. Then the main costly computational load in PC method is to make a projection onto the semi-definite cone. Exploiting the special structures of the relevant variational inequalities, the Levenberg-Marquardt type projection and contraction method is advantageous. Preliminary numerical tests up to 1000×1000 matrices indicate that the suggested approach is promising. 相似文献
18.
《Applied Mathematics Letters》2003,16(7):1003-1010
In this paper, we introduce and study a new class of generalized vector variational inequalities and complementarity problems for multivalued mappings. We prove the existence of solutions for this kind of vector variational inequality and discuss the relations between the solutions of the generalized vector variational inequalities and the solutions of generalized vector complementarity problems in Hausdorff topological vector spaces. Our results extend and improve some results in this field. 相似文献
19.
D. Goeleven 《Journal of Optimization Theory and Applications》1993,79(3):493-511
In this paper, we build an existence theory for linear variational inequalities associated with an operator which generalizes in Hilbert space the class of copositive plus matrices. We show how this theory can be used to study some important engineering problems governed by noncoercive variational inequalities.Thanks are due to Professor V. H. Nguyen for many valuable discussions. The author thanks the Associate Editor and the referees for their helpful suggestions 相似文献
20.
Muhammad Aslam Noor 《Optimization Letters》2009,3(3):437-451
In this paper, we introduce and consider a new system of general mixed variational inequalities involving three different
operators. Using the resolvent operator technique, we establish the equivalence between the general mixed variational inequalities
and the fixed point problems. We use this equivalent formulation to suggest and analyze some new explicit iterative methods
for this system of general mixed variational inequalities. We also study the convergence analysis of the new iterative method
under certain mild conditions. Since this new system includes the system of mixed variational inequalities involving two operators,
variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold
for these problems. Our results can be viewed as a refinement and improvement of the previously known results for variational
inequalities. 相似文献