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1.
§ 1 IntroductionThe problem of finding a point x* ∈S such that〈F(x* ) ,x -x* 〉≥ 0 for all x∈ S,(VIP)where S is a nonempty closed convex subset of Rn,F is a mapping from Rninto itself,and〈.,.〉denotes the inner productin Rn,is called the variational inequality problem and hasbeen widely used to study various equilibrium models arising in economic,operations re-search,transportation and regional sciences[1 ,2 ] .Many iterative methods for (VIP) havebeen developed,for example,project…  相似文献   

2.
1 IntroductionWe consider tlie variational inequality problelll, deuoted by VIP(X, F), wliicli is to find avector x* E X such thatF(X*)"(X -- X-) 2 0, VX E X, (1)where F: R" - R" is any vector-valued f11uction and X is a uonelllpty subset of R'.This problem has important applicatiolls. in equilibriun1 modeIs arising in fields such asecououtics, transportatioll scieuce alld operations research. See [1]. There exist mauy lllethodsfor solviug tlie variational li1equality problem VIP(X. …  相似文献   

3.
By using Fukushima‘s differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993. In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty, polyhedral,closed and convex is proposed. Armijo-type line search and trust region strategies as well as Fukushima‘s differentiable merit function are incorporated into the method. It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al. ,the method reduces to the basic Newton method and hence the rate of convergence is quadratic. Computational experiences show the efficiency of the proposed method.  相似文献   

4.
In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■Y is a set-valued mapping with closed graph.We establish the convergence criteria of the restricted inexact Newton-type method,which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Frechet derivative of f.Indeed,we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Frechet derivative of f is continuous and Lipschitz continuous as well as f+F is metrically regular.An application of this method to variational inequality is given.In addition,a numerical experiment is given which illustrates the theoretical result.  相似文献   

5.
1. IntroductionWe are concerned with the following variational inequality problem of finding amx E X such thatwhere f: R" - R" is assumed to be a continuously differentiable function, and X g R"is specified bywhere gi: R" -- R and h,-: R" - R are twice continuously differentiable functions.The variational inequality (1.1) is denoted by VI(X, f). An important special case ofVI(X, f) is the so--called nonlinear complementarity problem (NCP(f)) with X ~ R7 {x E R" I x 2 0}. Variational…  相似文献   

6.
Let c be a positive number.A continuous linear map F from a Banachspace X into a Banach space Y is said to be c-open if Y_1 F(X_c)where Y_1denotes the closed unit ball in Y and X_c the closed ball in X with centre at ori-gin and radius c.This is equivalent to require that the equation F_x=y has a so-lution x with ||x||≤||y|| whenever y∈Y. F is c-open for some c>0 if and only ifit is an open map.In this note we concern with a non-linear situation.Thus let  相似文献   

7.
曾六川 《东北数学》2004,20(1):30-40
Let X be a Banach space with a weakly continuous duality map Jφ,C a non-empty weakly compact convex subset of X, and T:(T(t):t∈S} an asymptotically nonexpansive type semigroup on C. In this paper, the inequality K∩F(T)≠0 is characterized, where K is a subset of C and F(T) is the set of all common fixed points of T. Furthermore, it is shown that an almost-orbit {u(t):t∈S} of T converges weakly to a point in F(T) if and only if {u(t):t∈S}is weakly asymptotically regular.  相似文献   

8.
EQUILIBRIUM PROBLEMS WITH LOWER AND UPPER BOUNDS IN TOPOLOGICAL SPACES   总被引:3,自引:0,他引:3  
1IntroductionLet X be a topological space and f:X×X→R{±∞}be a function.The equilibriumproblem(EP(X,f))is to find x?∈X such thatf(x?,y)≥0,?y∈X.(1)The EP(X,f)(1)includes many fundamental mathematical problems that arise from mechan-ics,engineering,economics,optimization,fixed point,saddle point,variational inequality andcomplementarity problem as special cases.See,for example,[1-4].In1999,Isac,Sehgal and Singh[5]raised the following open problem:given a nonemptyclosed subset K in a…  相似文献   

9.
求解不可微箱约束变分不等式的下降算法   总被引:2,自引:1,他引:1  
1 引 论 设X(?)Rn是非空闭集,F:Rn→Rn连续映射,变分不等式问题VI(X,F)是指:求x∈X,使 F(x)T(y-x)≥0,  (?)y∈X,(1)记指标集N=(1,2,…,n},当 X=[a,b]≡{x∈Rn|a≤xi≤bi,i∈N},(2)其中a={a1,a2,…,an}T,b={b1,b2,…,bn}T∈Rn时,VI(X,F)化为箱约束变分不等式VI(a,b,F).若ai=0,bi=+∞,i∈N,即X=R+n≡{x∈Rn|x≥0}时,VI(a,b,F)化为非线性  相似文献   

10.
Some modified Levitin-Polyak projection methods are proposed in this paper for solving monotone linear variational inequality x∈Ω,(x′-x)^T(Hx c)≤0,for any x′∈Ω.It is pointed out that there are similar methods for solving a general linear variational inequality.  相似文献   

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