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111.
彭宏 《吉首大学学报(自然科学版)》1996,17(3):14-17
在文献[1]中,引入符号矩阵,L分裂等全新概念.在半序Banach空间上建立了分《型单调遣代方法。本文是[1]工作的继续,讨论了该方法的唯一性。该理论包括了众多常见的单调这代方法的唯一性。 相似文献
112.
A coterie, which is used to realize mutual exclusion in distributed systems, is a family C of subsets such that any pair of subsets in C has at least one element in common, and such that no subset in C contains any other subset in C. Associate with a family of subsets C a positive Boolean function fc such that fc(x) = 1 if the Boolean vector x is equal to or greater than the characteristic vector of some subset in C, and 0 otherwise. It is known that C is a coterie if and only if fc is dual-minor, and is a non-dominated (ND) coterie if and only if fc is self-dual. We study in this paper the decomposition of a positive self-dual function into smaller positive self-dual functions, as it explains how to represent and how to construct the corresponding ND coterie. A key step is how to decompose a positive dual-minor function f into a conjunction of positive self-dual functions f1,f2,…, fk. In addition to the general condition for this decomposition, we clarify the condition for the decomposition into two functions f1, and f2, and introduce the concept of canonical decomposition. Then we present an algorithm that determines a minimal canonical decomposition, and a very simple algorithm that usually gives a decomposition close to minimal. The decomposition of a general self-dual function is also discussed. 相似文献
113.
In this paper, the existence of solutions to a class of fractional differential equations $D_{0+}^{\alpha}u(t)=h(t)f(t, u(t), D_{0+}^{\theta}u(t))$ is obtained by an efficient and simple monotone iteration method. At first, the existence of a solution to the problem above is guaranteed by finding a bounded domain $D_M$ on functions $f$ and $g$.
Then, sufficient conditions for the existence of monotone solution to the problem are established by applying monotone iteration method. Moreover, two efficient iterative schemes are proposed, and the convergence of the iterative process is proved by using the monotonicity assumption on $f$ and $g$. In particular, a new algorithm which combines Gauss-Kronrod quadrature method with cubic spline interpolation method is adopted to achieve the monotone iteration method in Matlab environment, and the high-precision approximate solution is obtained. Finally, the main results of the paper are illustrated by some numerical simulations, and the approximate solutions graphs are provided by using the iterative method. 相似文献
114.
彭宏 《吉首大学学报(自然科学版)》1992,(1)
在本文中,引入了符号矩阵、L分裂、混合分裂等全新的概念.在半序Banach空间上建立了统一的单调迭代方法的理论,研究了该方法的存在性和收敛性.该理论包括了众多常见的单调迭代理论 相似文献
115.
If Au = - div(a(x, Du)) is a monotone operator defined on the Sobolev space W1,P(R
n, 1 < p < + , with a(x,0) = 0 for a.e. x Rn, the capacity C_A(E,F) relative to A can be defined for every pair (E,F) of bounded sets in Rn with E F. The main properties of the set function CA(E,F) are investigated. In particular it is proved that CA(E,F) is increasing and countably subadditive with respect to E, decreasing with respect to F, and continuous, in a suitable sense, with respect to E and F. 相似文献
116.
Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities 总被引:13,自引:0,他引:13
In this paper, we study the relationship of some projection-type methods for monotone nonlinear variational inequalities and investigate some improvements. If we refer to the Goldstein–Levitin–Polyak projection method as the explicit method, then the proximal point method is the corresponding implicit method. Consequently, the Korpelevich extragradient method can be viewed as a prediction-correction method, which uses the explicit method in the prediction step and the implicit method in the correction step. Based on the analysis in this paper, we propose a modified prediction-correction method by using better prediction and correction stepsizes. Preliminary numerical experiments indicate that the improvements are significant. 相似文献
117.
F.A. McRae 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6093-6096
Using the method of upper and lower solutions, an existence result for IVP of Riemann-Liouville fractional differential equation is studied. Also, the monotone iterative technique is developed and the existence results for maximal and minimal solutions are obtained. 相似文献
118.
本文用新的方法证明了Sianey H.Kumg不等式猜想的正确性,同时举例说明了相关文献结果的不合理性,并得到了修正结果. 相似文献
119.
X. Wang 《Journal of Optimization Theory and Applications》2009,141(3):661-676
The extragradient method uses only the values of the function in the variational inequality to solve it. In many real-life
problems, the functions do not have explicit expressions and their evaluations are expensive. Therefore, it is important and
practical to reduce the number of function evaluations used in these problems. In order to do this, we present some modifications
to one existing extragradient method. First, we analyze the limit of the projection along a direction onto a closed convex
set. Then, using the obtained result, we give a horizontal asymptotic property of an estimated function to the one measuring
the progress in each iteration. From this property, a Newton search as well a self-adjusted relaxation procedure are introduced
with an improved steplength into the extragradient method. Besides the theoretical background, numerical results are given
to show the progress of the modified method.
This work was supported by National Natural Science Foundation of China 10571083 and Doctoral Fund of Ministry of Education
of China 20060284001. 相似文献
120.
In this paper we consider two quasilinear boundary value problems. The first is vector valued and has periodic boundary conditions.
The second is scalar valued with nonlinear boundary conditions determined by multivalued maximal monotone maps. Using the
theory of maximal monotone operators for reflexive Banach spaces and the Leray-Schauder principle we establish the existence
of solutions for both problems. 相似文献