共查询到20条相似文献,搜索用时 29 毫秒
1.
In this paper, we introduce the notions of Levitin?CPolyak (LP) well-posedness and Levitin?CPolyak well-posedness in the generalized sense, for a parametric quasivariational inequality problem of the Minty type. Metric characterizations of LP well-posedness and generalized LP well-posedness, in terms of the approximate solution sets are presented. A parametric gap function for the quasivariational inequality problem is introduced and an equivalence relation between LP well-posedness of the parametric quasivariational inequality problem and that of the related optimization problem is obtained. 相似文献
2.
Nguyen Van Hung Vo Minh Tam Dumitru Baleanu 《Mathematical Methods in the Applied Sciences》2020,43(7):4614-4626
In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new. 相似文献
3.
In this paper, we study Levitin–Polyak type well-posedness for generalized quasivariational inequality problems with explicit constraints. Four types of Levitin–Polyak well-posedness will be introduced. Various criteria and characterizations will be derived for these types of Levitin–Polyak well-posedness. 相似文献
4.
We define the concept of reproducible map and show that, whenever the constraint map defining the quasivariational inequality (QVI) is reproducible then one can characterize the whole solution set of the QVI as a union of solution sets of some variational inequalities (VI). By exploiting this property, we give sufficient conditions to compute any solution of a generalized Nash equilibrium problem (GNEP) by solving a suitable VI. Finally, we define the class of pseudo-Nash equilibrium problems, which are (not necessarily convex) GNEPs whose solutions can be computed by solving suitable Nash equilibrium problems. 相似文献
5.
Phan Quoc Khanh Le Minh Luu Tran Trinh Minh Son 《Nonlinear Analysis: Real World Applications》2013,14(3):1643-1654
We define kinds of approximate solutions of a traffic network problem and obtain relations to approximate solutions of the corresponding quasivariational inequality. Using these results we establish sufficient conditions for the Tikhonov well-posedness in the sense of Levitin–Polyak of our traffic network problem. 相似文献
6.
In this paper, we introduce and study a few classes of generalized multivalued nonlinear quasivariational inclusions and generalized nonlinear quasivariational inequalities, which include many classes of variational inequalities, quasivariational inequalities and variational inclusions as special cases. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for finding the approximate solutions of these classes of quasivariational inclusions and quasivariational inequalities. We establish the existence of solutions for this generalized nonlinear quasivariational inclusions involving both relaxed Lipschitz and strongly monotone and generalized pseudocontractive mappings and obtain the convergence of iterative sequences generated by the algorithms. Under certain conditions, we derive the existence of a unique solution for the generalized nonlinear quasivariational inequalities and obtain the convergence and stability results of the Noor type perturbed iterative algorithm. The results proved in this paper represent significant refinements and improvements of the previously known results in this area. 相似文献
7.
L. Gong 《Journal of Optimization Theory and Applications》1991,70(2):365-375
This paper studies some stability properties for the generalized quasivariational inequality problem. The study of this topic is motivated by the work of Harker and Pang (Ref. 1). A global stability result is obtained for problems satisfying certain conditions.The author would like to express his gratitude to the referees for helpful suggestions for the revision of the paper. 相似文献
8.
The paper deals with a generalization of a vector quasivariational inequality. An existence theorem for its solutions is established; it is based on a kind of minimax inequality, which is here established for continuous affine mappings and differs from previous results. Fan's section theorem for set-valued mappings is extended. An application for an equilibrium problem of a network with vector-valued cost functions is given.This research was supported by the National Nature Science Foundation of China. 相似文献
9.
M. B. Lignola 《Journal of Optimization Theory and Applications》2006,128(1):119-138
In this paper, two concepts of well-posedness for quasivariational inequalities having a unique solution are introduced. Some
equivalent characterizations of these concepts and classes of well-posed quasivariational inequalities are presented. The
corresponding concepts of well-posedness in the generalized sense are also investigated for quasivariational inequalities
having more than one solution
The author is grateful to an anonymous referee for valuable comments. 相似文献
10.
In this article, we introduce and study different types of Levitin–Polyak well-posedness for a constrained inverse quasivariational inequality problem. Criteria and characterizations for these types of well-posedness for inverse quasivariational inequality problems are given. Su?cient conditions for the Levitin–Polyak well-posedness of inverse quasivariational inequality problems are also established. 相似文献
11.
This paper presents a new iterative algorithm for a quasivariational inequality system related to HJB equation. A domain decomposition method based on this algorithm is proposed. The convergence theorems have been established. 相似文献
12.
In this paper, stability of a parametric quasivariational inequality of the Minty type is studied via various sufficient conditions
characterizing upper and lower semicontinuity of the solution sets as well as the approximate solution sets. Sufficient conditions
ensuring upper semicontinuity of the approximate solution sets of an optimization problem with quasivariational inequality
constraints are also presented. 相似文献
13.
Lai-Jiu Lin 《Journal of Global Optimization》2007,38(1):21-39
In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result,
we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium
problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical
program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and
systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints.
This research was supported by the National Science Council of the Republic of China. 相似文献
14.
J.I. Baltaev 《Journal of Mathematical Analysis and Applications》2008,345(2):917-928
We consider a reaction-diffusion system with implicit unilateral boundary conditions introduced by U. Mosco. We show that global continua of stationary spatially nonhomogeneous solutions bifurcate in the domain of parameters where bifurcation in the case of classical boundary conditions is excluded. The problem is formulated as a quasivariational inequality and the proof is based on the Leray-Schauder degree. 相似文献
15.
The quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown.
As special cases, we obtain several results on the existence of solutions of a general vector ideal (proper, Pareto, weak)
quasi-optimization problems, of quasivariational inequalities, and of vector quasi-equilibrium problems. Further, we prove
theorems on the existence for solutions of the sum of these inclusions. As corollaries, we shall show several results on the
existence of solutions to another problems in the vector optimization problems concerning multivalued mappings.
This work was supported by the National Science Council of the Republic of China and the Academy of Sciences and Technologies
of Vietnam.
The authors wish to express their gratitude to the referees for their valuable suggestions. 相似文献
16.
Ulisse Stefanelli 《Journal of Differential Equations》2006,229(1):204-228
This note addresses a class of abstract quasivariational evolution equations taking into account nonlocality with respect to time. We present an existence result for suitably weak solutions to such problems, which extend previous contributions. The existence argument relies on some order technique and exploits a fixed point result for multivalued applications in ordered spaces. Moreover, we discuss the application of our results to classes of ODE and parabolic PDE problems. 相似文献
17.
It is well known that the generalized Nash equilibrium problem, a model for multi-leader–follower games, can be reformulated as a quasivariational inequality. We show that, in fact, a reformulation in terms of a variational inequality can be obtained in the general setting of quasiconvex nondifferentiable decision functions. An existence result is deduced. 相似文献
18.
I. P. Ryazantseva 《Differential Equations》2008,44(7):1006-1017
For quasivariational inequalities of special form in a Hilbert space, we construct a continuous second-order method and a discrete version of this method, prove the strong convergence of these methods, and indicate the possibility of obtaining estimates for the convergence rate. We separately study the convergence of the continuous method under the assumption that the operators describing the quasivariational inequality to be solved are potential. We establish sufficient conditions for the unique solvability of the nonlinear problems determining these methods. 相似文献
19.
L. C. Ceng N. Hadjisavvas S. Schaible J. C. Yao 《Journal of Optimization Theory and Applications》2008,139(1):109-125
In this paper, we introduce concepts of well-posedness, and well-posedness in the generalized sense, for mixed quasivariational-like
inequalities where the underlying map is multivalued. We give necessary and sufficient conditions for the various kinds of
well-posedness to occur. Our results generalize and strengthen previously found results for variational and quasivariational
inequalities.
Part of this research was done while the second and the third authors were visiting the Department of Applied Mathematics,
National Sun-Yat-Sen University. The authors wish to thank the Department for its hospitality. 相似文献
20.
In this paper, we aim to suggest the new concept of well-posedness for the general parametric quasi-variational inclusion problems (QVIP). The corresponding concepts of well-posedness in the generalized sense are also introduced and investigated for QVIP. Some metric characterizations of well-posedness for QVIP are given. We prove that under suitable conditions, the well-posedness is equivalent to the existence of uniqueness of solutions. As applications, we obtain immediately some results of well-posedness for the parametric quasi-variational inclusion problems, parametric vector quasi-equilibrium problems and parametric quasi-equilibrium problems. 相似文献