共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we use the Wiener–Hopf equations technique to suggest and analyze new iterative methods for solving general quasimonotone variational inequalities. These new methods differ from previous known methods for solving variational inequalities. 相似文献
2.
考虑和分析了一类求解广义集值变分不等式的一类新的外梯度算法,该方法包含几个新的和已知的算法作为特例.改进了求解变分不等式及其相关的优化问题的已有的许多结果. 相似文献
3.
In this paper, we use the auxiliary principle technique to suggest a new class of predictor-corrector algorithms for solving multivalued variational inequalities. The convergence of the proposed methods requires only the partially-relaxed strong monotonicity of the operator, which is weaker than cocoercivity. As special cases, we obtain a number of known and new results for solving various classes of variational inequalities. 相似文献
4.
In this paper, we introduce and study a new class of variational inequalities, which is called the generalized mixed variational inequality. Using essentially the resolvent operator concept, we establish the equivalence between the generalized mixed variational inequalities and the system of resolvent equations. This equivalence is used to suggest a number of new iterative algorithms for solving the variational inequalities. Several special cases are discussed which can be obtained from the main results of this paper. 相似文献
5.
Muhammad Aslam Noor 《Journal of Applied Mathematics and Computing》2010,32(1):83-95
In this paper, we introduce and study a new class of variational inequalities involving three operators, which is called the extended general variational inequality. Using the projection technique, we show that the extended general variational inequalities are equivalent to the fixed point and the extended general Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze a number of projection iterative methods for solving the extended general variational inequalities. We also consider the convergence of these new methods under some suitable conditions. Since the extended general variational inequalities include general variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems. 相似文献
6.
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
7.
M. A. Noor 《Mathematical and Computer Modelling》2000,31(13):139-19
In this paper, we use the auxiliary principle technique to suggest a class of predictor-corrector methods for solving general mixed variational inequalities. The convergence of the proposed methods only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving various classes of variational inequalities and related problems. 相似文献
8.
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
9.
MUHAMMAD ASLAM NOOR 《Journal of Global Optimization》2000,18(1):75-89
In this paper, we suggest and analyze a number of resolvent-splitting algorithms for solving general mixed variational inequalities by using the updating technique of the solution. The convergence of these new methods requires either monotonicity or pseudomonotonicity of the operator. Proof of convergence is very simple. Our new methods differ from the existing splitting methods for solving variational inequalities and complementarity problems. The new results are versatile and are easy to implement. 相似文献
10.
《Mathematical and Computer Modelling》1999,29(3):95-100
In this paper, we suggest and analyze a new iterative method for solving monotone mixed variational inequations using the resolvent operator technique. This new method can be viewed as an extension of the extragradient methods for solving the monotone variational inequalities. 相似文献
11.
在无穷维Hillbert空间中研究了一类单调型变分不等式,把求单调型变分不等式解的问题转化为求强单调变分不等式的解,建立了一种新的迭代算法,并证明了由算法生成的迭代序列强收敛于单调变分不等式的解,从而推广了所列文献中的许多重要结果. 相似文献
12.
Javad Balooee 《Journal of Optimization Theory and Applications》2017,172(3):774-801
In this paper, we turn our attention to formulating and studying a new class of variational inequalities in a nonconvex setting, called regularized nonconvex mixed variational inequalities. By using the auxiliary principle technique, some new predictor corrector methods for solving such class of regularized nonconvex mixed variational inequalities are suggested and analyzed. The study of convergence analysis of the proposed iterative algorithms requires either pseudomonotonicity or partially mixed relaxed and strong monotonicity of the operator involved in regularized nonconvex mixed variational inequalities. As a consequence of our main results, we provide the correct versions of the algorithms and results presented in the literature. 相似文献
13.
Yonghong Yao Muhammad Aslam Noor Khalida Inayat Noor Yeong-Cheng Liou Huma Yaqoob 《Acta Appl Math》2010,110(3):1211-1224
In this paper, we introduce a new system of general variational inequalities in Banach spaces. We establish the equivalence
between this system of variational inequalities and fixed point problems involving the nonexpansive mapping. This alternative
equivalent formulation is used to suggest and analyze a modified extragradient method for solving the system of general variational
inequalities. Using the demi-closedness principle for nonexpansive mappings, we prove the strong convergence of the proposed
iterative method under some suitable conditions. 相似文献
14.
《Journal of Computational and Applied Mathematics》2001,135(1):111-124
In this paper, we suggest and analyze a number of four-step resolvent splitting algorithms for solving general mixed variational inequalities by using the updating technique of the solution. The convergence of these new methods requires either monotonicity or pseudomonotonicity of the operator. Proof of convergence is very simple. Our new methods differ from the existing splitting methods for solving variational inequalities and complementarity problems. The new results are versatile and are easy to implement. 相似文献
15.
Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2003,277(2):379-394
In this paper, we consider and analyze a new class of extragradient-type methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is weaker condition than monotonicity. Our proof of convergence is very simple as compared with other methods. The proposed methods include several new and known methods as special cases. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. 相似文献
16.
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
17.
In this paper, we introduce and study a class of differential vector variational inequalities in finite dimensional Euclidean spaces. We establish a relationship between differential vector variational inequalities and differential scalar variational inequalities. Under various conditions, we obtain the existence and linear growth of solutions to the scalar variational inequalities. In particular we prove existence theorems for Carathéodory weak solutions of the differential vector variational inequalities. Furthermore, we give a convergence result on Euler time-dependent procedure for solving the initial-value differential vector variational inequalities. 相似文献
18.
Muhammad Aslam Noor Khalida Inayat Noor Th.M Rassias 《Journal of Mathematical Analysis and Applications》1998,220(2):804
In this paper, we introduce and study a new class of variational inequalities, which is called the generalized set-valued mixed variational inequality. The resolvent operator technique is used to establish the equivalence among generalized set-valued variational inequalities, fixed point problems, and the generalized set-valued resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area. 相似文献
19.
《Journal of Computational and Applied Mathematics》2005,182(2):316-326
In this paper, we introduce and consider a new class of variational inequalities, known as the hemivariational-like inequalities. It is shown that the hemivariational-like inequalities include hemivariational inequalities, variational-like inequalities and the classical variational inequalities as special cases. The auxiliary principle is used to suggest and analyze some iterative methods for solving hemivariational-like inequalities under mild conditions. The results obtained in this paper can be considered as a novel application of the auxiliary principle technique. 相似文献
20.
In this paper, we use the auxiliary principle technique to suggest a class of predictorcorrector methods for solving general mixed variational inequalities. The convergence of the proposed methods only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. From special cases, we obtain various known and new results for solving various classes of variational inequalities and related problems.AMS Subject Classification (1991): 49J40, 90C33. 相似文献