共查询到20条相似文献,搜索用时 31 毫秒
1.
一类椭圆型变分不等式离散问题的迭代算法 总被引:10,自引:1,他引:9
根据一类椭圆型变分不等式离散问题所具有的非线性特征,提出了一种简明快速的迭代算法,该方法在解决障碍问题及流体润滑油膜破裂自然边值问题等工程应用问题时具有较高的效率。 相似文献
2.
General variational inequalities and nonexpansive mappings 总被引:1,自引:0,他引:1
Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2007,331(2):810-822
In this paper, we suggest and analyze some three-step iterative schemes for finding the common elements of the set of the solutions of the Noor variational inequalities involving two nonlinear operators and the set of the fixed points of nonexpansive mappings. We also consider the convergence analysis of the suggested iterative schemes under some mild conditions. Since the Noor variational inequalities include variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an refinement and improvement of the previously known results. 相似文献
3.
Livinus U. Uko 《Mathematical Programming》1996,73(3):251-268
We give some convergence results on the generalized Newton method (referred to by some authors as Newton's method) and the
chord method when applied to generalized equations. The main results of the paper extend the classical Kantorovich results
on Newton's method to (nonsmooth) generalized equations. Our results also extend earlier results on nonsmooth equations due
to Eaves, Robinson, Josephy, Pang and Chan.
We also propose inner-iterative schemes for the computation of the generalized Newton iterates. These schemes generalize popular
iterative methods (Richardson's method, Jacobi's method and the Gauss-Seidel method) for the solution of linear equations
and linear complementarity problems and are shown to be convergent under natural generalizations of classical convergence
criteria.
Our results are applicable to equations involving single-valued functions and also to a class of generalized equations which
includes variational inequalities, nonlinear complementarity problems and some nonsmooth convex minimization problems. 相似文献
4.
该文提出并分析了用广义投影方法解Noor型广义变分不等式问题.在较弱的条件下考虑了一个迭代格式的收敛性.由于广义变分不等式包含了许多变分不等式和相补问题为特例,因此该文得出的结果可以应用到这些问题中.这些结果是以前众多学者所做工作的完善和改进. 相似文献
5.
In this article we introduce a new class of equilibrium problems known as mixed quasi invex equilibrium (equilibrium-like) problems with trifunction. This class of equilibrium problems includes invex equilibrium problems, variational inequalities and variational-like inequalities as special cases. We use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under mild conditions. Our results represent significant and important refinements of the previously known results. 相似文献
6.
Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2005,302(2):463-475
In this paper, we introduce a new class of equilibrium problems, known as invex equilibrium problems in the setting of invexity. This class of equilibrium problems includes equilibrium problems, variational inequalities and variational-like inequalities as special cases. We use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under some mild conditions. We also consider the concept of well-posedness for invex equilibrium problems. Our results represent significant and important refinements of the previously known results. 相似文献
7.
Muhammad Aslam Noor 《Journal of Applied Mathematics and Computing》2010,34(1-2):57-70
In this paper, we consider a class of variational inequalities which is called the general mixed variational inequality. It is known that the general mixed variational inequalities are equivalent to the fixed point problems. This equivalent formulation is used to suggest and analyze some three-step iterative schemes for finding the common element of the set of fixed points of a nonexpansive mappings and the set of solutions of the mixed variational inequalities. We also study the convergence criteria of three-step iterative method under some mild conditions. Our results include the previous results as special cases and may be considered as an improvement and refinement of the previously known results. 相似文献
8.
A. A. Alikhanov 《Computational Mathematics and Mathematical Physics》2016,56(4):561-575
A family of difference schemes for the fractional-order diffusion equation with variable coefficients is considered. By the method of energetic inequalities, a priori estimates are obtained for solutions of finite-difference problems, which imply the stability and convergence of the difference schemes considered. The validity of the results is confirmed by numerical calculations for test examples. 相似文献
9.
Rolf Dieter Grigorieff 《Mathematische Nachrichten》1988,135(1):93-101
For finite difference schemes of compact form on nonuniform grids approximating m-th order two-point boundary value problems stability inequalities are proved which use a norm analogous to the Spijker-norm in the case of multistep methods. The results are applied to a number of finite difference schemes for which they establish a higher order of convergence than naively expected. 相似文献
10.
关于非线性不等式组Levenberg-Marquardt算法的收敛性(英文) 总被引:2,自引:1,他引:1
本文研究了一类非线性不等式组的求解问题.利用一列目标函数两次可微的参数优化问题来逼近非线性不等式组的解,光滑Levenberg-Marquardt方法来求解参数优化问题,在一些较弱的条件下证明了文中算法的全局收敛性,数值实例显示文中算法效果较好. 相似文献
11.
Muhammad Aslam Noor 《Journal of Applied Mathematics and Computing》2011,35(1-2):1-9
In this paper, we introduce and study a new class of equilibrium problems, known as mixed quasi nonconvex equilibrium problems. We use the auxiliary principle technique to suggest and analyze some iterative schemes for solving nonconvex equilibrium problems. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier known results for solving equilibrium problems and variational inequalities involving the convex sets. 相似文献
12.
Muhammad Aslam Noor 《Journal of Applied Mathematics and Computing》2007,23(1-2):183-191
In this paper, we introduce and study a new class of equilibrium problems, known as regularized mixed quasi equilibrium problems. We use the auxiliary principle technique to suggest and analyze some iterative schemes for regularized equilibrium problems. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving equilibrium problems and variational inequalities involving the convex sets. 相似文献
13.
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
14.
Muhammad Aslam Noor 《Journal of Global Optimization》2001,19(2):141-150
In this paper, we suggest and analyze a class of iterative schemes for solving multivalued quasi variational inclusions using the resolvent operator method. As special cases, we obtain a number of known and new iterative schems for solving variational inequalities and related optimization problems. The results obtained in this represent an improvement and a significant refinement of previously known results. 相似文献
15.
《Optimization》2012,61(6):749-776
We make use of the auxiliary problem principle to develop iterative algorithms for solving equilibrium problems. The first one is an extension of the extragradient algorithm to equilibrium problems. In this algorithm the equilibrium bifunction is not required to satisfy any monotonicity property, but it must satisfy a certain Lipschitz-type condition. To avoid this requirement we propose linesearch procedures commonly used in variational inequalities to obtain projection-type algorithms for solving equilibrium problems. Applications to mixed variational inequalities are discussed. A special class of equilibrium problems is investigated and some preliminary computational results are reported. 相似文献
16.
17.
《Journal of Computational and Applied Mathematics》1997,84(2):189-206
The paper deals with parabolic differential-functional equations. Initial-boundary value problems are considered with impulses given in fixed points. We prove theorems on difference-functional impulsive inequalities generated by original problems.Explicit finite difference schemes are used to approximate the solutions of the original problems. We give sufficient conditions for the convergence of sequences of approximate solutions under the assumptions that the right-hand sides satisfy the nonlinear estimates of the Perron type with respect to the functional argument. In proof of the convergence of difference methods we apply theorems on difference-functional impulsive inequalities. 相似文献
18.
We study the finite-difference approximation for the quasi-variational inequalities for a stochastic game involving discrete actions of the players and continuous and discrete payoff. We prove convergence of iterative schemes for the solution of the discretized quasi-variational inequalities, with estimates of the rate of convergence (via contraction mappings) in two particular cases. Further, we prove stability of the finite-difference schemes, and convergence of the solution of the discrete problems to the solution of the continuous problem as the discretization mesh goes to zero. We provide a direct interpretation of the discrete problems in terms of finite-state, continuous-time Markov processes. 相似文献
19.
We present and analyze subspace correction methods for the solution of variational inequalities of the second kind and apply
these theoretical results to non smooth contact problems in linear elasticity with Tresca and non-local Coulomb friction.
We introduce these methods in a reflexive Banach space, prove that they are globally convergent and give error estimates.
In the context of finite element discretizations, where our methods turn out to be one- and two-level Schwarz methods, we
specify their convergence rate and its dependence on the discretization parameters and conclude that our methods converge
optimally. Transferring this results to frictional contact problems, we thus can overcome the mesh dependence of some fixed-point
schemes which are commonly employed for contact problems with Coulomb friction. 相似文献
20.
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