共查询到20条相似文献,搜索用时 31 毫秒
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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
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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
4.
Q. Z. Yang 《Journal of Optimization Theory and Applications》2006,130(3):547-549
Verma introduced a system of nonlinear variational inequalities and proposed projection methods to solve it. This system reduces to a variational inequality problem under certain conditions. So, at least in form, it can be regarded as a extension of a variational inequality problem. In this note, we show that solving this system coincides exactly with solving a variational inequality problem. Therefore, we conclude that it suffices to study the corresponding variational inequalities.This work was supported by the National Natural Science Foundation of China, Grant 10571134.Communicated by M. J. Balas 相似文献
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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
6.
In this paper, we introduce and consider a new system of general variational inequalities involving four different operators. Using the projection operator technique, we suggest and analyze some new explicit iterative methods for this system of 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 variational inequalities involving three 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
7.
In this paper, we first introduce the system of generalized implicit variational inequalities and prove the existence of its solution. Then we derive existence results for systems of generalized variational and variational like inequalities and system of variational inequalities. As applications, we establish some existence results for a solution to the system of optimization problems which includes the Nash equilibrium problem as a special case 相似文献
8.
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
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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
10.
In this paper we first revisit a classical problem of computing variational splines. We propose to compute local variational splines in the sense that they are interpolatory splines which minimize the energy norm over a subinterval. We shall show that the error between local and global variational spline interpolants decays exponentially over a fixed subinterval as the support of the local variational spline increases. By piecing together these locally defined splines, one can obtain a very good C0 approximation of the global variational spline. Finally we generalize this idea to approximate global tensor product B-spline interpolatory surfaces. 相似文献
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In this article, we introduce and consider a general system of variational inequalities. Using the projection technique, we suggest and analyse new iterative methods for this system of 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 variational inequalities involving the single operator, variational inequalities and related optimization problems as special cases, results obtained in this article continue to hold for these problems. Our results improve and extend the recent ones announced by many others. 相似文献
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Weak minimizers,minimizers and variational inequalities for set-valued functions. A blooming wreath?
Giovanni P. Crespi 《Optimization》2017,66(12):1973-1989
Recently, necessary and sufficient conditions in terms of variational inequalities have been introduced to characterize minimizers of convex set-valued functions. Similar results have been proved for a weaker concept of minimizers and weaker variational inequalities. The implications are proved using scalarization techniques that eventually provide original problems, not fully equivalent to the set-valued counterparts. Therefore, we try, in the course of this note, to close the network among the various notions proposed. More specifically, we prove that a minimizer is always a weak minimizer, and a solution to the stronger variational inequality always also a solution to the weak variational inequality of the same type. As a special case, we obtain a complete characterization of efficiency and weak efficiency in vector optimization by set-valued variational inequalities and their scalarizations. Indeed, this might eventually prove the usefulness of the set optimization approach to renew the study of vector optimization. 相似文献
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Chih-Sheng Chuang 《Numerical Functional Analysis & Optimization》2017,38(3):306-326
In this article, we study the generalized split variational inclusion problem. For this purpose, motivated by the projected Landweber algorithm for the split equality problem, we first present a simultaneous subgradient extragradient algorithm and give related convergence theorems for the proposed algorithm. Next, motivated by the alternating CQ-algorithm for the split equality problem, we propose another simultaneous subgradient extragradient algorithm to study the general split variational inclusion problem. As applications, we consider the split equality problem, split feasibility problem, split variational inclusion problem, and variational inclusion problem in Hilbert spaces. 相似文献
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The set-valued variational inequality problem is very useful in economics theory and nonsmooth optimization. In this paper, we introduce some gap functions for set-valued variational inequality problems under suitable assumptions. By using these gap functions we derive global error bounds for the solution of the set-valued variational inequality problems. Our results not only generalize the previously known results for classical variational inequalities from single-valued case to set-valued, but also present a way to construct gap functions and derive global error bounds for set-valued variational inequality problems. 相似文献
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In this paper, we introduce and study a new class of variational inequalities, which is called the generalized mixed variational inequality. Using essentially the resolvent operator concept, we establish the equivalence between the generalized mixed variational inequalities and the system of resolvent equations. This equivalence is used to suggest a number of new iterative algorithms for solving the variational inequalities. Several special cases are discussed which can be obtained from the main results of this paper. 相似文献
16.
In a recent paper, Domokos and Kolumbán introduced variational inequalities with operator solutions to provide a suitable
unified approach to several kinds of variational inequality and vector variational inequality in Banach spaces. Inspired by
their work, in this paper, we further develop the new scheme of vector variational inequalities with operator solutions from
the single-valued case into the multi-valued one. We prove the existence of solutions of generalized vector variational inequalities
with operator solutions and generalized quasi-vector variational inequalities with operator solutions. Some applications to
generalized vector variational inequalities and generalized quasi-vector variational inequalities in a normed space are also
provided. 相似文献
17.
《Optimization》2012,61(3):355-367
In this article, we consider equivalence properties between various kinds of lexicographic variational inequalities. By employing various concepts of monotonicity, we show that the usual sequential variational inequality is equivalent to the direct lexicographic variational inequality or to the dual lexicographic variational inequality. We establish several existence results for lexicographic variational inequalities. Also, we introduce the lexicographic complementarity problem and establish its equivalence with the lexicographic variational inequality. We illustrate our approach by several examples of applications to vector transportation and vector spatial equilibrium problems. 相似文献
18.
This paper introduces the concept of exceptional family for nonlinear variational inequality problems. Among other things, we show that the nonexistence of an exceptional family is a sufficient condition for the existence of a solution to variational inequalities. This sufficient condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. From the results in this paper, we believe that the concept of exceptional families of variational inequalities provides a new powerful tool for the study of the existence theory for variational inequalities. 相似文献
19.
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
20.
Levitin-Polyak well-posedness of variational inequalities 总被引:1,自引:0,他引:1
In this paper we consider the Levitin-Polyak well-posedness of variational inequalities. We derive a characterization of the Levitin-Polyak well-posedness by considering the size of Levitin-Polyak approximating solution sets of variational inequalities. We also show that the Levitin-Polyak well-posedness of variational inequalities is closely related to the Levitin-Polyak well-posedness of minimization problems and fixed point problems. Finally, we prove that under suitable conditions, the Levitin-Polyak well-posedness of a variational inequality is equivalent to the uniqueness and existence of its solution. 相似文献