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1.
In this paper, we introduce and consider a new system of nonlinear variational inequalities involving two different operators. Using the parallel projection technique, we suggest and analyze an iterative method for this system of variational inequalities. We establish a convergence result for the proposed method under certain conditions. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities. 相似文献
2.
Dao-Jun Wen 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2292-2297
In this paper, we introduce and consider a new generalized system of nonconvex variational inequalities with different nonlinear operators. We establish the equivalence between the generalized system of nonconvex variational inequalities and the fixed point problems using the projection technique. This equivalent alternative formulation is used to suggest and analyze a general explicit projection method for solving the generalized system of nonconvex variational inequalities. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities. 相似文献
3.
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
4.
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
5.
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.
Muhammad Aslam Noor 《Applicable analysis》2013,92(5):777-786
In this article, we introduce and consider a new system of general nonconvex variational inequalities involving four different operators. We use the projection operator technique to establish the equivalence between the system of general nonconvex variational inequalities and the fixed points problem. This alternative equivalent formulation is used to suggest and analyse some new explicit iterative methods for this system of nonconvex 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 nonconvex variational inequalities, variational inequalities and related optimization problems as special cases, results obtained in this article continue to hold for these problems. Our results can be viewed as a refinement and an improvement of the previously known results for variational inequalities. 相似文献
7.
Muhammad Aslam Noor Abdellah Bnouhachem Saleem Ullah 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):3728-3738
It is well known that the general variational inequalities are equivalent to the fixed point problems and the Wiener-Hopf equations. In this paper, we use these alternative equivalent formulations to suggest and analyze some new self-adaptive iterative methods for solving the general variational inequalities. Our results can be viewed as a significant extension of the previously known results for variational inequalities. An example is given to illustrate the efficiency of the proposed method. 相似文献
8.
9.
Abdellah Bnouhachem Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2006,324(2):1195-1212
In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor-corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method. 相似文献
10.
In this paper, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of a nonlinear variational inclusion and the set of common fixed points of a finite family of strictly pseudo-contractive mappings which solves some variational inequality in a real Banach space. Our results improve and extend the corresponding results announced by many others. 相似文献
11.
Muhammad Aslam Noor 《Optimization Letters》2009,3(3):411-418
In this paper, we introduce and consider a new class of variational inequalities, which is called the nonconvex variational
inequalities. We establish the equivalence between the nonconvex variational inequalities and the fixed-point problems using
the projection technique. This equivalent formulation is used to discuss the existence of a solution of the nonconvex variational
inequalities. We also use this equivalent alternative formulation to suggest and analyze a new iterative method for solving
the nonconvex variational inequalities. We also discuss the convergence of the iterative method under suitable conditions.
Our method of proof is very simple as compared with other techniques. 相似文献
12.
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
13.
Muhammad Aslam Noor Eisa Al-Said 《Journal of Computational and Applied Mathematics》2011,235(9):3104-3108
In this paper, we introduce and consider a new class of variational inequalities, which are called the nonconvex variational inequalities. Using the projection technique, we suggest and analyze an extragradient method for solving the nonconvex variational inequalities. We show that the extragradient method is equivalent to an implicit iterative method, the convergence of which requires only pseudo-monotonicity, a weaker condition than monotonicity. This clearly improves on the previously known result. Our method of proof is very simple as compared with other techniques. 相似文献
14.
This paper centres on the effectiveness of the variational iteration method and its modifications for numerically solving
the chaotic Chen system, which is a three-dimensional system of ODEs with quadratic nonlinearities. This research implements
the multistage variational iteration method with an emphasis on the new multistage hybrid of variational iteration method
with Adomian polynomials. Numerical comparisons are made between the multistage variational iteration method, the multistage
variational iteration method using the Adomian’s polynomials and the classic fourth-order Runge-Kutta method. Our work shows
that the new multistage hybrid provides good accuracy and efficiency with a performance that surpasses that of the multistage
variational iteration method. 相似文献
15.
主要研究带有非齐次边界条件的拟线性椭圆方程组的正解问题,在合适参数条件下,用变分方法和流形方法得到该椭圆方程组正解的存在性和多解性.结论推广了近期发表的结果. 相似文献
16.
《Optimization》2012,61(5):981-998
ABSTRACTIn this paper, we introduce several new extragradient-like approximation methods for solving variational inequalities in Hilbert spaces. Our algorithms are based on Tseng's extragradient method, subgradient extragradient method, inertial method, hybrid projection method and shrinking projection method. Strong convergence theorems are established under appropriate conditions. Our results extend and improve some related results in the literature. In addition, the efficiency of our algorithms is shown through numerical examples which are defined by the hybrid projection methods. 相似文献
17.
In this paper, we apply an existence theorem for the variational inclusion problem to study the existence results for the variational intersection problems in Ekeland’s sense and the existence results for some variants of set-valued vector Ekeland variational principles in a complete metric space. Our results contain Ekeland’s variational principle as a special case and our approaches are different to those for any existence theorems for such problems. 相似文献
18.
In this paper, we study strict feasibility of a bifunction variational inequality. It is proved that a monotone bifunction variational inequality has a nonempty and bounded solution set if and only if it is strictly feasible. Stable solvability of the bifunction variational inequality is discussed under strict feasibility assumption when the domain set is perturbed. Our results generalize earlier results on the classical variational inequality to the case of the bifunction variational inequality. 相似文献
19.
A proximal point method for solving mixed variational inequalities is suggested and analyzed by using the auxiliary principle technique. It is shown that the convergence of the proposed method requires only the pseudomonotonicity of the operator, which is a weaker condition than monotonicity. As special cases, we obtain various known and new results for solving variational inequalities and related problems. Our proof of convergence is very simple as compared with other methods. 相似文献
20.
《Applied Mathematics Letters》2003,16(7):1003-1010
In this paper, we introduce and study a new class of generalized vector variational inequalities and complementarity problems for multivalued mappings. We prove the existence of solutions for this kind of vector variational inequality and discuss the relations between the solutions of the generalized vector variational inequalities and the solutions of generalized vector complementarity problems in Hausdorff topological vector spaces. Our results extend and improve some results in this field. 相似文献