带上下界均衡问题解的存在性及H?lder连续性

本文利用Ekeland变分原理分别在紧集和非紧集上获得了带上下界均衡问题解的存在性定理,从而进一步回答了Isac等人提出的公开问题.此外,还在度量空间中研究了带上下界均衡问题解的局部H?lder连续性.以上所有结果不要求相关映射和集合具有任何凸性.     

加权流形上加权p-Laplace特征值问题的第一特征值下界估计（英文）

本文研究了加权流形上加权p-Laplacian特征值问题的第一特征值下界估计的问题.利用余面积公式、Cavalieri原理以及Federer-Fleming定理,获得了由Cheeger常数或等周常数确定的第一特征值的下界估计.     

仿射不变量W_i(K)W_i(K~*)的下界估计

对于所有凸体与每一个i,寻找仿射不变量Wi(K)Wi(K*)下界的问题,是一个至今未能解决的公开问题.本文考虑了仿射不变量Wi(K)Wi(K*)的下界是与凸体K本身有关的常数的情形,并利用混合体积与对偶混合体积的关系理论,对仿射不变量Wi(K)Wi(K*)进行了讨论,获得了仿射不变量Wi(K)Wi(K*)的一个下界.作为应用,其对偶仿射不变量Wi(K)Wi(K*)的下界也被建立.     

再论仿射不变量$W_{i}(K)W_{i}(K^{})$的下界估计

对于所有凸体与每一个$i$, 寻找仿射不变量$W_{i}(K)W_{i}(K^{*})$下界的问题是一个至今未能完全解决的公开问题. 最近,赵长健考虑了仿射不变量$W_{i}(K)W_{i}(K^{*})$的下界是与凸体$K$本身有关的常数的情形, 并利用混合体积与对偶混合体积的关系理论, 对仿射不变量$W_{i}(K)W_{i}(K^{*})$的下界进行了讨论. 本文进一步讨论仿射不变量$W_{i}(K)W_{i}(K^{*})$的下界估计, 并对具有正的连续曲率且包含原点为其内点的凸体\!$K$, 获得了仿射不变量$W_{i}(K)W_{i}(K^{*})$的几个不同精度的下界, 同时给出了著名的Bourgain-Milman 不等式中通用常数$c$的具体表示值.最后提出了两个公开问题.     

加权流形上加权p-Laplace特征值问题的第一特征值下界估计

本文研究了加权流形上加权p-Laplacian特征值问题的第一特征值下界估计的问题.利用余面积公式、Cavalieri原理以及Federer-Fleming定理,获得了由Cheeger常数或等周常数确定的第一特征值的下界估计.     

一种求解半向量二层规划问题下界的算法

针对下层为线性多目标规划问题的一类半向量二层规划问题的乐观模型,利用线性规划的对偶理论,将其转化为一个等价的单层优化问题.然后考虑后者的一个松弛问题,提出了一个可以获得该问题下界的简单算法,从而给出了原二层规划问题的一个下界.最后,通过两个数值算例说明了所提出算法的可行性.     

Keller-Segel拋物系统解的爆破现象

本文研究了Keller-Segel拋物系统在Robin边界条件下解的爆破问题.利用微分不等式技术,推导了一个一阶微分不等式,并由此不等式获得了在R~3上Keller-Segel抛物系统解的爆破时间的下界.在一些适当的约束条件下,也获得了在R~N(N3)上Keller-Segel抛物系统爆破解显式下界     

具有梯度源和非局部源的反应扩散方程解的爆破时刻下界北大核心CSCD

对于反应扩散方程解的爆破时刻研究,不仅具有理论意义,而且与安全地控制生产,控制种群密度以及环境趋化治理等实际问题密切相关.该文考虑了一类具有梯度源和非局部源的反应扩散方程解的爆破时刻下界.首先,假设区域为高维空间中的具有光滑边界的有界凸区域;其次,通过构造合适的辅助函数,利用一阶微分不等式技术和Sobolev不等式,得出解在有限时刻发生爆破时的爆破时刻下界;最后,通过两个应用实例来解释说明文中所获得的抽象结论.     

关于正矩阵的最大特征值的包含定理及其应用

1　引　　言由于矩阵特征值问题在弹性动力学和自动控制等领域均已获得广泛的应用,所以关于矩阵特征值的计算方法及其上、下界的估计均为人们所关注.随着计算机的发展,有关矩阵特征值的各种有效算法应运而生[1].至于特征值的上、下界的估计问题,虽然也有很多成果[2-4],且它们在数学上都有一定的理论意义和应用价值,但常因其界限太宽而缺少工程价值.鉴于此,笔者利用文[3]引入的同步向量这一概念,讨论了正矩阵的最大特征值的上、下界的确定问题,获得了这类矩阵最大特征值的较为精确的包含定理,又与幂法[1]相结合,给出了非亏损正矩阵的最大特征…     

一种基于匈牙利算法的二次分配问题求解方法

二次分配问题(Quadratic assignment problem,QAP)属于NP-hard组合优化难题.二次分配问题的线性化及下界计算方法,是求解二次分配问题的重要途径.以Frieze-Yadegar线性化模型和Gilmore-Lawler下界为基础,详细论述了二次分配问题线性化模型的结构特征,并分析了Gilmore-Lawler下界值往往远离目标函数最优值的原因.在此基础上,提出一种基于匈牙利算法的二次分配问题对偶上升下界求解法.通过求解QAPLIB中的部分实例,说明了方法的有效和可行性.     

抽象经济均衡问题解的存在性及其算法

本文首先研究一类新的向量均衡问题,利用截口定理与KKM定理两种不同的工具证明此类均衡问题解的存在性,接着,把这类向量均衡问题推广到更为一般的情形,随后讨论了具有上下界的均衡问题,它是由Isac,Sehgal和Singh于1999年提出的一个公开问题,本文在一定条件下获得了一个新的解的存在性定理,并构造了一个迭代算法,讨论了算法的收敛性。     

Continuity for vector optimization problems with equilibrium constraints

The concept of vector optimization problems with equilibrium constraints (VOPEC) is introduced. By using the continuity results of the approximate solution set to the equilibrium problem, we obtain the same results of the marginal map and the approximate value in VOPEC (e) for vector-valued mapping.     

On nonconvex equilibrium problems

In this paper, we introduce a new class of equilibrium problems, known as mixed quasi nonconvex equilibrium problems. We suggest some iterative schemes for solving nonconvex equilibrium problems by using the auxiliary principle technique. The convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity. As special cases, we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems.     

Equilibrium problems with lower and upper bounds

In this paper, we obtain some existence results of equilibrium problems with lower and upper bounds by employing a fixed-point theorem due to Ansari and Yao [1] and Ky Fan Lemma [2], respectively. Our results give answers to the open problem raised by Isac, Sehgal and Singh [3].     

On the proximal point method for equilibrium problems in Hilbert spaces

We analyse a proximal point method for equilibrium problems in Hilbert spaces, improving upon previously known convergence results. We prove global weak convergence of the generated sequence to a solution of the problem, assuming existence of solutions and rather mild monotonicity properties of the bifunction which defines the equilibrium problem, and we establish existence of solutions of the proximal subproblems. We also present a new reformulation of equilibrium problems as variational inequalities ones.     

Multivalued general equilibrium problems

In this paper, we use the auxiliary principle technique to suggest some new classes of iterative algorithms for solving multivalued equilibrium problems. The convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity. As special cases, we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems. Since multivalued equilibrium problems include equilibrium, variational inequality and complementarity problems as specials cases, our results continue to hold for these problems.     

Multivalued Regularized Equilibrium Problems

In this paper, we introduce a new class of equilibrium problems known as the multivalued regularized equilibrium problems. We use the auxiliary principle technique to suggest some iterative methods for solving multivalued regularized equilibrium problems. The convergence of the proposed methods is studied under some mild conditions. As special cases, we obtain a number of known and new results for solving various classes of regularized equilibrium problems and related optimization problems.     

Efficient estimates of the solutions of perturbed control problems

In this paper, we obtain estimates of the solutions for a sequence of strongly convex extremal problems. As applications of our abstract results, we consider optimal control problems with various types of perturbations. We estimate the solutions of problems with perturbations in the state equation and in the control constraining set. A singularly perturbed problem and a problem with perturbed time delay parameter are studied.     

Characterizations of Solutions for Vector Equilibrium Problems

In this paper, we characterize the solutions of vector equilibrium problems as well as dual vector equilibrium problems. We establish also vector optimization problem formulations of set-valued maps for vector equilibrium problems and dual vector equilibrium problems, which include vector variational inequality problems and vector complementarity problems. The set-valued maps involved in our formulations depend on the data of the vector equilibrium problems, but not on their solution sets. We prove also that the solution sets of our vector optimization problems of set-valued maps contain or coincide with the solution sets of the vector equilibrium problems.     

Duality for generalized equilibrium problem

We introduce a generalized equilibrium problem (GEP) that allow us to develop a robust dual scheme for this problem, based on the theory of conjugate functions. We obtain a unified dual analysis for interesting problems. Indeed, the Lagrangian duality for convex optimization is a particular case of our dual problem. We establish necessary and sufficient optimality conditions for GEP that become a well-known theorem given by Mosco and the dual results obtained by Morgan and Romaniello, which extend those introduced by Auslender and Teboulle for a variational inequality problem.