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161.
A globally convergent Newton method for solving strongly monotone variational inequalities 总被引:14,自引:0,他引:14
Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method. 相似文献
162.
163.
The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator 总被引:2,自引:0,他引:2
Wei-ping Sun Wei-gao GeDepartment of Applied Mathematics Beijing Institute of Technology Beijing China 《应用数学学报(英文版)》2002,18(2):341-348
Abstract The existence of infinitely many solutions to Sturm-Liouville boundary value problem with aLaplacian-like operator is studied by applying generalized polar coordinates. 相似文献
164.
Neil S. TrudingerXu-Jia Wang 《Journal of Functional Analysis》2002,193(1):1-23
In this paper, we continue previous investigations into the theory of Hessian measures. We extend our weak continuity result to the case of mixed k-Hessian measures associated with k-tuples of k-convex functions, on domains in Euclidean n-space, k=1,2,…,n. Applications are given to capacity, quasicontinuity, and the Dirichlet problem, with inhomogeneous terms, continuous with respect to capacity or combinations of Dirac measures. 相似文献
165.
H. R. Ebrahimi-Vishki M. A. Pourabdollah 《Proceedings of the American Mathematical Society》1997,125(7):2171-2174
The purpose of this paper is to introduce an algebra of functions on a semitopological semigroup and to study these functions from the point of view of universal semigroup compactification. We show that the corresponding semigroup compactification of this algebra is universal with respect to the property of being a nilpotent group.
166.
罗尔定理证明一类存在性问题 总被引:1,自引:0,他引:1
提出罗尔定理证明一类存在性问题的方法,采用拉格朗日中值定理或柯西中值定理来证明这类问题往往需要构造精巧的辅助函数,我们还指出了这种方法的一般性. 相似文献
167.
图G(V,E)的一个k-正常全染色f叫做一个k-点强全染色当且仅当对任意v∈V(G), N[v]中的元素被染不同色,其中N[v]={u|uv∈V(G)}∪{v}.χTvs(G)=min{k|存在图G的k- 点强全染色}叫做图G的点强全色数.对3-连通平面图G(V,E),如果删去面fo边界上的所有点后的图为一个树图,则G(V,E)叫做一个Halin-图.本文确定了最大度不小于6的Halin- 图和一些特殊图的的点强全色数XTvs(G),并提出了如下猜想:设G(V,E)为每一连通分支的阶不小于6的图,则χTvs(G)≤△(G) 2,其中△(G)为图G(V,E)的最大度. 相似文献
168.
Tatsien Li 《Mathematical Methods in the Applied Sciences》2006,29(13):1543-1553
By means of a direct and constructive method based on the theory of semi‐global C2 solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
169.
We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential
operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the
Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems. 相似文献
170.
Giovanni Cupini Marcello Guidorzi Cristina Marcelli 《Journal of Differential Equations》2007,243(2):329-348
Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained. 相似文献