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481.
Manoj Changat 《Discrete Applied Mathematics》2010,158(5):426-2609
The geodesic interval function I of a connected graph allows an axiomatic characterization involving axioms on the function only, without any reference to distance, as was shown by Nebeský [20]. Surprisingly, Nebeský [23] showed that, if no further restrictions are imposed, the induced path function J of a connected graph G does not allow such an axiomatic characterization. Here J(u,v) consists of the set of vertices lying on the induced paths between u and v. This function is a special instance of a transit function. In this paper we address the question what kind of restrictions could be imposed to obtain axiomatic characterizations of J. The function J satisfies betweenness if w∈J(u,v), with w≠u, implies u∉J(w,v) and x∈J(u,v) implies J(u,x)⊆J(u,v). It is monotone if x,y∈J(u,v) implies J(x,y)⊆J(u,v). In the case where we restrict ourselves to functions J that satisfy betweenness, or monotonicity, we are able to provide such axiomatic characterizations of J by transit axioms only. The graphs involved can all be characterized by forbidden subgraphs. 相似文献
482.
The purpose of this paper is to study the weak Galerkin finite element method for a class of quasilinear elliptic problems. The weak Galerkin finite element scheme is proved to have a unique solution with the assumption that guarantees the corresponding operator to be strongly monotone and Lipschitz-continuous. An optimal error estimate in a mesh-dependent energy norm is established. Some numerical results are presented to confirm the theoretical analysis. 相似文献
483.
484.
A unifying geometric solution framework and complexity analysis for variational inequalities 总被引:1,自引:0,他引:1
In this paper, we propose a concept of polynomiality for variational inequality problems and show how to find a near optimal solution of variational inequality problems in a polynomial number of iterations. To establish this result, we build upon insights from several algorithms for linear and nonlinear programs (the ellipsoid algorithm, the method of centers of gravity, the method of inscribed ellipsoids, and Vaidya's algorithm) to develop a unifying geometric framework for solving variational inequality problems. The analysis rests upon the assumption of strong-f-monotonicity, which is weaker than strict and strong monotonicity. Since linear programs satisfy this assumption, the general framework applies to linear programs.Preparation of this paper was supported, in part, by NSF Grant 9312971-DDM from the National Science Foundation. 相似文献
485.
In this paper we study a class of numerical methods used to solve two-point boundary value problems on nonuniform grids. Particular attention is devoted to positive solutions, i.e. conditions under which the solutions of the problem are positive. Applications to steady states of air pollution problems are also referred to. 相似文献
486.
The Monotone Iterative Technique and Periodic Boundary Value Problem for First Order Impulsive Functional Differential Equations 总被引:1,自引:0,他引:1
This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence
of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential
equations.
Received June 15, 1998, Revised April 29, 2000, Accepted July 18, 2000 相似文献
487.
A continuation method for (strongly) monotone variational inequalities 总被引:11,自引:0,他引:11
We consider the variational inequality problem, denoted by VIP(X, F), whereF is a strongly monotone function and the convex setX is described by some inequality (and possibly equality) constraints. This problem is solved by a continuation (or interior-point) method, which solves a sequence of certain perturbed variational inequality problems. These perturbed problems depend on a parameter > 0. It is shown that the perturbed problems have a unique solution for all values of > 0, and that any sequence generated by the continuation method converges to the unique solution of VIP(X,F) under a well-known linear independence constraint qualification (LICQ). We also discuss the extension of the continuation method to monotone variational inequalities and present some numerical results obtained with a suitable implementation of this method. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V. 相似文献
488.
魏利 《河北大学学报(自然科学版)》1998,(3)
从研究算子方程f∈Tx+Sx的可解性出发,给出了带紧扰动的极大单调算子的一些映射定理,这些定理推广和改进了以往的有关结论。 相似文献
489.
490.
Nguyen BUONG 《数学学报(英文版)》2005,21(5):1001-1004
A class of a posteriori parameter choice strategies for the operator version of Tiknonov regularization (including variants of Morozov's and Arcangeli's methods) is proposed and used in investigating the rate of convergence of the regularized solution for ill-posed nonlinear equation involving a monotone operator in Banach space. 相似文献