共查询到20条相似文献,搜索用时 15 毫秒
1.
Wei-Qi Deng 《Numerical Algorithms》2014,66(4):779-791
By using a new technique, namely, a specific way of choosing the indexes of the involved mappings, we introduce a new iterative algorithm for approximating common fixed points of a countable family of multi-valued totally quasi-?-asymptotically nonexpansive mappings and obtain a strong convergence theorem under some suitable conditions. As application, an iterative solution to a system of generalized mixed equilibrium problems is studied. The results extend those of other authors, in which the involved mapping consists of just a single one. 相似文献
2.
Nan -Jing Huang 《Journal of Applied Mathematics and Computing》1998,5(2):315-329
In this paper, we introduce and study a new class of random completely generalized strongly nonlinear quasi - complementarity problems with non-compact valued random fuzzy mappings and construct some new iterative algorithms for this kind of random fuzzy quasi-complementarity problems. We also prove the existence of random solutions for this class of random fuzzy quasicomplementarity problems and the convergence of random iterative sequences generated by the algorithms. 相似文献
3.
《Applied Mathematics Letters》2006,19(3):294-297
In this work, we consider a generalized nonlinear variational-like inequality problem in the setting of locally convex topological vector spaces and prove the existence of its solutions. 相似文献
4.
The nonlinear complementarity problem is generalized by replacing the usual nonnegative ordering ofR
n
by an ordering generated by a convex cone. Two new classes of operators are introduced, each of which is used to guarantee the existence of a solution to the generalized problem. The new classes can be seen to be broader than previously studied classes. In addition, conditions are presented under which the solution set of the generalized linear complementarity problem is shown to have at most a finite number of solutions.This research was partially supported by National Science Foundation, Grant No. GP-16293, and constitutes part of the junior author's doctoral thesis. The authors are indebted to Dr. Carlton E. Lemke for many helpful discussions. 相似文献
5.
A new method for solving a system of generalized nonlinear variational inequalities in Banach spaces
The purpose of this paper is by using the generalized projection approach to introduce an iterative scheme for finding a solution to a system of generalized nonlinear variational inequality problem. Under suitable conditions, some existence and strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces. The results presented in the paper improve and extend some recent results. 相似文献
6.
Let f and g be continuously differentiable functions on R
n
. The nonlinear complementarity problem NCP(f,g), 0≤f(x)⊥g(x)≥0, arises in many applications including discrete Hamilton-Jacobi-Bellman equations and nonsmooth Dirichlet problems. A
popular method to find a solution of the NCP(f,g) is the generalized Newton method which solves an equivalent system of nonsmooth equations F(x)=0 derived by an NCP function. In this paper, we present a sufficient and necessary condition for F to be Fréchet differentiable, when F is defined by the “min” NCP function, the Fischer-Burmeister NCP function or the penalized Fischer-Burmeister NCP function.
Moreover, we give an explicit formula of an element in the Clarke generalized Jacobian of F defined by the “min” NCP function, and the B-differential of F defined by other two NCP functions. The explicit formulas for generalized differentials of F lead to sharper global error bounds for the NCP(f,g). 相似文献
7.
M. A. Golberg 《Journal of Optimization Theory and Applications》1973,11(2):146-158
A functional is given which generalizes the Rayleigh quotient to eigenvalue problems for linear operators where the eigenvalue parameter appears nonlinearly. Particular emphasis is given to the development of perturbation-type results for eigenvalues and characteristic values which generalize the classical results. Applications are made to eigenvalue and characteristic value problems for integral and matrix operators and to the critical length problem for integral operators. Both symmetric and nonsymmetric operators are treated.The author would like to acknowledge the work of Gloria Golberg in the preparation of this paper. 相似文献
8.
9.
As a generalization of almost perfect nonlinear functions, generalized almost perfect nonlinear (GAPN) functions defined over finite fields of odd characteristic have also important applications in cryptography and finite geometry. In this paper, we mainly focus on GAPN power functions, and a new class of such function (up to EA equivalence) is obtained. Furthermore, using our method, almost all the known GAPN power functions can be confirmed in a simple way. 相似文献
10.
In this paper, a new hybrid method is proposed for solving nonlinear complementarity problems (NCP) with P
0 function. In the new method, we combine a smoothing nonmonotone trust region method based on a conic model and line search
techniques. We reformulate the NCP as a system of semismooth equations using the Fischer-Burmeister function. Using Kanzow’s
smooth approximation function to construct the smooth operator, we propose a smoothing nonmonotone trust region algorithm
of a conic model for solving the NCP with P
0 functions. This is different from the classical trust region methods, in that when a trial step is not accepted, the method
does not resolve the trust region subproblem but generates an iterative point whose steplength is defined by a line search.
We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under a nonsingularity
condition, the superlinear convergence of the algorithm is established without a strict complementarity condition. 相似文献
11.
An iterative method for solving generalized nonlinear complementarity problems (Ref. 1) involving stronglyK-copositive operators is introduced. Conditions are presented which guarantee the convergence of the method; in addition, the sequence of iterates is used to prove the existence of a solution to the problem under conditions not included in the previous study. Separate consideration is given to the generalized linear complementarity problem.This research was partially supported by National Science Foundation, Grant No. GP-16293. This paper constitutes part of the junior author's doctoral thesis written at Rensselaer Polytechnic Institute. Research support was provided by an NDEA Fellowship and an RPI Fellowship. 相似文献
12.
利用光滑对称扰动Fischer-Burmeister函数将广义非线性互补问题转化为非线性方程组,提出新的光滑化拟牛顿法求解该方程组.然后证明该算法是全局收敛的,且在一定条件下证明该算法具有局部超线性(二次)收敛性.最后用数值实验验证了该算法的有效性. 相似文献
13.
14.
Abdellah Bnouhachem Muhammad Aslam Noor Mohamed Khalfaoui Sheng Zhaohan 《Applied mathematics and computation》2009,215(2):695-706
In this paper, we propose a new modified logarithmic-quadratic proximal (LQP) method for solving nonlinear complementarity problems (NCP). We suggest using a prediction-correction method to solve NCP. The predictor is obtained via solving the LQP system approximately under significantly relaxed accuracy criterion and the new iterate is computed by using a new step size αk. Under suitable conditions, we prove that the new method is globally convergent. We report preliminary computational results to illustrate the efficiency of the proposed method. This new method can be considered as a significant refinement of the previously known methods for solving nonlinear complementarity problems. 相似文献
15.
A new smoothing quasi-Newton method for nonlinear complementarity problems is presented. The method is a generalization of Thomas’ method for smooth nonlinear systems and has similar properties as Broyden's method. Local convergence is analyzed for a strictly complementary solution as well as for a degenerate solution. Presented numerical results demonstrate quite similar behavior of Thomas’ and Broyden's methods. 相似文献
16.
Xiuyun Zheng Jiarong Shi Wei Yang Qingyan Yin 《Journal of Applied Mathematics and Computing》2017,54(1-2):277-295
Based on a new symmetrically perturbed smoothing function, the generalized nonlinear complementarity problem defined on a polyhedral cone is reformulated as a system of smoothing equations. Then we suggest a new nonmonotone derivative-free line search and combine it into the smoothing Broyden-like method. The proposed algorithm contains the usual monotone line search as a special case and can overcome the difficult of smoothing Newton methods in solving the smooth equations to some extent. Under mild conditions, we prove that the proposed algorithm has global and local superlinear convergence. Furthermore, the algorithm is locally quadratically convergent under suitable assumptions. Preliminary numerical results are also reported. 相似文献
17.
A linesearch (steplength) algorithm for unconstrained nonlinear least squares problems is described. To estimate the steplength
inside the linesearch algorithm a new method that interpolates the residual vector is used together with a standards method
that interpolates the sums of squares.
Numerical results are reported that point out the advantage with the new steplength estimation method. 相似文献
18.
In this paper, we introduce and study a new class of completely generalized mildly nonlinear complementarity problems for fuzzy mappings and construct some new iterative algorithms. We also show the existence of solution and the convergence of iterative sequences generated by the algorithms. Our results extend some recent results of Noor, Chang and Huang. 相似文献
19.
对广义非线性Schroedinger方程提出了一种新的差分格式。揭示了该差分格式满足两个守恒律,并证明该格式的收敛性和稳定性.数值实验结果表明,新的差分格式优于Crank-Nicolson格式以及Zhang Fei等人提出的格式。 相似文献