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1.
The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. (J. Optim. Theory Appl. 148, 318–335, 2011), replaces the second projection onto the feasible set of the VI, in the extragradient method, with a subgradient projection onto some constructible half-space. Since the method has been introduced, many authors proposed extensions and modifications with applications to various problems. In this paper, we introduce a modified subgradient extragradient method by improving the stepsize of its second step. Convergence of the proposed method is proved under standard and mild conditions and primary numerical experiments illustrate the performance and advantage of this new subgradient extragradient variant. 相似文献
2.
In this paper, we propose an easily implementable algorithm in Hilbert spaces for solving some classical monotone variational inequality problem over the set of solutions of mixed variational inequalities. The proposed method combines two strategies: projected subgradient techniques and viscosity-type approximations. The involved stepsizes are controlled and a strong convergence theorem is established under very classical assumptions. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints. 相似文献
3.
Numerical Algorithms - It is well known that the algorithms with using a proximal operator can be not convergent for monotone variational inequality problems in the general case. Malitsky (Optim.... 相似文献
4.
In this paper, we introduce an algorithm as combination between the subgradient extragradient method and inertial method for solving variational inequality problems in Hilbert spaces. The weak convergence of the algorithm is established under standard assumptions imposed on cost operators. The proposed algorithm can be considered as an improvement of the previously known inertial extragradient method over each computational step. The performance of the proposed algorithm is also illustrated by several preliminary numerical experiments. 相似文献
5.
A projected subgradient method for solving generalized mixed variational inequalities 总被引:1,自引:0,他引:1
We consider the projected subgradient method for solving generalized mixed variational inequalities. In each step, we choose an εk-subgradient uk of the function f and wk in a set-valued mapping T, followed by an orthogonal projection onto the feasible set. We prove that the sequence is weakly convergent. 相似文献
6.
We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints.
Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker
type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error
bound constraint qualification, the no nonzero abnormal multiplier constraint qualification, the generalized Mangasarian-Fromovitz
constraint qualification, the strong regularity constraint qualification and the linear constraint qualification. We then
apply these results to the multiobjective optimization problem with complementarity constraints and the multiobjective bilevel
programming problem.
Received: November 2000 / Accepted: October 2001 Published online: December 19, 2002
Key Words. Multiobjective optimization – Variational inequality – Complementarity constraint – Constraint qualification – Bilevel programming
problem – Preference – Utility function – Subdifferential calculus – Variational principle
Research of this paper was supported by NSERC and a University of Victoria Internal Research Grant
Research was supported by the National Science Foundation under grants DMS-9704203 and DMS-0102496
Mathematics Subject Classification (2000): Sub49K24, 90C29 相似文献
7.
LiangXiming LiFei XuChengxian 《高校应用数学学报(英文版)》2000,15(4):470-482
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
8.
A numerical approach to optimization problems with variational inequality constraints 总被引:7,自引:0,他引:7
Optimization problems with variational inequality constraints are converted to constrained minimization of a local Lipschitz function. To this minimization a non-differentiable optimization method is used; the required subgradients of the objective are computed by means of a special adjoint equation. Besides tests with some academic examples, the approach is applied to the computation of the Stackelberg—Cournot—Nash equilibria and to the numerical solution of a class of quasi-variational inequalities.Corresponding author. 相似文献
9.
Ling-ling Huang San-yang Liu Wei-feng Gao 《Applied mathematics and computation》2010,217(7):3216-3225
This paper presents a modified projection method for solving variational inequalities, which can be viewed as an improvement of the method of Yan, Han and Sun [X.H. Yan, D.R. Han, W.Y. Sun, A modified projection method with a new direction for solving variational inequalities, Applied Mathematics and Computation 211 (2009) 118-129], by adopting a new prediction step. Under the same assumptions, we establish the global convergence of the proposed algorithm. Some preliminary computational results are reported. 相似文献
10.
Numerical Algorithms - In this paper, basing on the subgradient extragradient method and inertial method with line-search process, we introduce two new algorithms for finding a common element of... 相似文献
11.
Numerical Algorithms - In a very interesting paper (SIAM J. Control Optim. 37(3): 765–776, 1999), Solodov and Svaiter introduced an effective projection algorithm with linesearch for finding... 相似文献
12.
13.
In this paper, we propose a new projection method for solving variational inequality problems, which can be viewed as an improvement of the method of Li et al. [M. Li, L.Z. Liao, X.M. Yuan, A modified projection method for co-coercive variational inequality, European Journal of Operational Research 189 (2008) 310-323], by adopting a new direction. Under the same assumptions as those in Li et al. (2008), we establish the global convergence of the proposed algorithm. Some preliminary computational results are reported, which illustrated that the new method is more efficient than the method of Li et al. (2008). 相似文献
14.
This paper presents a secant method, based on R. B. Wilson's formula for the solution of optimization problems with inequality constraints. Global convergence properties are ensured by grafting the secant method onto a phase I - phase II feasible directions method, using a rate of convergence test for crossover control.This research was sponsored by the National Science Foundation, Grant No. ENG-73-08214 and Grant No. (RANN)-ENV-76-04264, and by the Joint Services Electronics Program. Contract No. F44620-76-C-0100. 相似文献
15.
GAOZIYOU(高自友)(NorthernJiaotongUniversity,Beijing100044,China)LAIYANLIAN(赖炎连)(InstituteofAppliedMathematics,theChineseAcademyo... 相似文献
16.
Numerical Algorithms - In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in... 相似文献
17.
Shih-sen Chang H.W. Joseph Lee Chi Kin Chan 《Nonlinear Analysis: Theory, Methods & Applications》2009
In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings. The results presented in the paper extend and improve some recent results of Yao and Yao [Y.Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2) (2007) 1551–1558], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.075], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for Equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006) 506–515], Su, Shang and Qin [Y.F. Su, M.J. Shang, X.L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and Chang, Cho and Kim [S.S. Chang, Y.J. Cho, J.K. Kim, Approximation methods of solutions for equilibrium problem in Hilbert spaces, Dynam. Systems Appl. (in print)]. 相似文献
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19.
交替方向法是求解可分离结构变分不等式问题的经典方法之一, 它将一个大型的变分不等式问题分解成若干个小规模的变分不等式问题进行迭代求解. 但每步迭代过程中求解的子问题仍然摆脱不了求解变分不等式子问题的瓶颈. 从数值计算上来说, 求解一个变分不等式并不是一件容易的事情.因此, 本文提出一种新的交替方向法, 每步迭代只需要求解一个变分不等式子问题和一个强单调的非线性方程组子问题. 相对变分不等式问题而言, 我们更容易、且有更多的有效算法求解一个非线性方程组问题. 在与经典的交替方向法相同的假设条件下, 我们证明了新算法的全局收敛性. 进一步的数值试验也验证了新算法的有效性. 相似文献
20.
In this paper, using the Gabriel–Moré smoothing function of the median function, a smooth homotopy method for solving nonsmooth equation reformulation of bounded box constrained variational inequality problem VIP(l,u,F) is given. Without any monotonicity condition on the defining map F, for starting point chosen almost everywhere in Rn, existence and convergence of the homotopy pathway are proven. Nevertheless, it is also proven that, if the starting point is chosen to be an interior point of the box, the proposed homotopy method can also serve as an interior point method. 相似文献