与(p,q)-Laplace算子相关的非线性Dirichlet椭圆系解的存在性及其迭代构造(英文)

利用变分不等式解的存在性的结论,研究了一类与(p,q)-Laplace算子相关的非线性Dirichlet椭圆系解的存在性的抽象结论.然后,利用极大单调算子零点的结论,构造了一种迭代格式强收敛到上述椭圆系的解.本文所研究的椭圆系及所用方法是对以往一些工作的推广和补充.     

New subgradient extragradient methods for solving monotone bilevel equilibrium problems

ABSTRACT

In this paper, we propose new subgradient extragradient methods for finding a solution of a strongly monotone equilibrium problem over the solution set of another monotone equilibrium problem which usually is called monotone bilevel equilibrium problem in Hilbert spaces. The first proposed algorithm is based on the subgradient extragradient method presented by Censor et al. [Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148:318–335]. The strong convergence of the algorithm is established under monotone assumptions of the cost bifunctions with Lipschitz-type continuous conditions recently presented by Mastroeni in the auxiliary problem principle. We also present a modification of the algorithm for solving an equilibrium problem, where the constraint domain is the common solution set of another equilibrium problem and a fixed point problem. Several fundamental experiments are provided to illustrate the numerical behaviour of the algorithms and to compare with others.     

Maximal independent sets in caterpillar graphs

A caterpillar graph is a tree in which the removal of all pendant vertices results in a chordless path. In this work, we determine the number of maximal independent sets (mis) in caterpillar graphs. For a general graph, this problem is #P—complete. We provide a polynomial time algorithm to generate the whole family of mis in a caterpillar graph. We also characterize the independent graph (intersection graph of mis) and the clique graph (intersection graph of cliques) of complete caterpillar graphs.     

Convergence analysis of a hybrid Mann iterative scheme with perturbed mapping for variational inequalities and fixed point problems

The purpose of this article is to investigate the problem of finding a common element of the set of fixed points of a non-expansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce a hybrid Mann iterative scheme with perturbed mapping which is based on the well-known Mann iteration method and hybrid (or outer approximation) method. We establish a strong convergence theorem for three sequences generated by this hybrid Mann iterative scheme with perturbed mapping. Utilizing this theorem, we also construct an iterative process for finding a common fixed point of two mappings, one of which is non-expansive and the other taken from the more general class of Lipschitz pseudocontractive mappings.     

On the weak convergence of iterative sequences for generalized equilibrium problems and strictly pseudocontractive mappings

In this article we consider the problem of finding a common element in the solution set of generalized equilibrium problems, in the solution set of the classical variational inequality and in the fixed point set of strictly pseudocontractive mappings. Weak convergence theorems of common elements are established in real Hilbert spaces.     

Rectangularity and paramonotonicity of maximally monotone operators

Maximally monotone operators play a key role in modern optimization and variational analysis. Two useful subclasses are rectangular (also known as star monotone) and paramonotone operators, which were introduced by Brezis and Haraux, and by Censor, Iusem and Zenios, respectively. The former class has a useful range of properties while the latter class is of importance for interior point methods and duality theory. Both notions are automatic for subdifferential operators and known to coincide for certain matrices; however, more precise relationships between rectangularity and paramonotonicity were not known. Our aim is to provide new results and examples concerning these notions. It is shown that rectangularity and paramonotonicity are actually independent. Moreover, for linear relations, rectangularity implies paramonotonicity but the converse implication requires additional assumptions. We also consider continuous linear monotone operators, and we point out that in the Hilbert space both notions are automatic for certain displacement mappings.     

A variant of forward-backward splitting method for the sum of two monotone operators with a new search strategy

In this paper, we propose variants of Forward-Backward splitting method for finding a zero of the sum of two operators. A classical modification of Forward-Backward method was proposed by Tseng, which is known to converge when the forward and the backward operators are monotone and with Lipschitz continuity of the forward operator. The conceptual algorithm proposed here improves Tseng’s method in some instances. The first and main part of our approach, contains an explicit Armijo-type search in the spirit of the extragradient-like methods for variational inequalities. During the iteration process, the search performs only one calculation of the forward-backward operator in each tentative of the step. This achieves a considerable computational saving when the forward-backward operator is computationally expensive. The second part of the scheme consists in special projection steps. The convergence analysis of the proposed scheme is given assuming monotonicity on both operators, without Lipschitz continuity assumption on the forward operator.     

求解CPM网络计划的最大网络时差

CPM网络计划的网络时差表示项目中各工序实际可使用的机动时间的总和(绝非理论上机动时间的简单加总),即CPM网络计划的总机动时间,它决定着在总工期不变的前提下,所有工序实际可以达到的最大工期的总和,与项目的成本管理和时间管理密切相关。网络时差是变量,取决于各工序的时间进度安排,说明可以通过调整工序的时间进度来决定该时差的取值,特别是其最大值,进而实现成本和时间优化。本文首先从新的角度分析了网络时差的含义;然后,在此基础上设计了求解最大网络时差的算法,其思路为,通过建立和分析最大网络时差模型,将其转化为特殊的“时间-费用权衡问题”,进而可运用Fulkerson算法等经典算法求解;最后,通过应用举例对该算法进行了演示。     

具控制结构的向量拟均衡系统

引入一类向量伪单调映射,在Hausdorff拓扑线性空间中,利用向量映射的锥连续条件与极大元定理,讨论具控制结构的向量拟均衡问题系统,研究该问题的有效解及强解,得到这两类解的存在性与解集的紧性,并建立这两类解之间的联系。     

Effect of magnetic field on poroelastic bone model for internal remodeling

This paper studies the effects of the magnetic field and the porosity on a poroelastic bone model for internal remodeling. The solution of the internal bone remodeling process induced by a magnetic field is presented. The bone is treated as a poroelastic material by Biot’s formulation. Based on the theory of small strain adaptive elasticity, a theoretical approach for the internal remodeling is proposed. The components of the stresses, the displacements, and the rate of internal remodeling are obtained in analytical forms, and the numerical results are represented graphically. The results indicate that the effects of the magnetic field and the porosity on the rate of internal remodeling in bone are very pronounced.