Critical duality

We look for a general framework in which the Ekeland duality can be formulated. We propose a scheme in which the parameter sets are provided with a coupling function which induces a conjugacy. The decision spaces are not supposed to have any special structure. We examine several examples. In particular, we consider some special classes of generalized convex functions.     

Systems of equilibrium problems with applications to new variants of Ekeland’s variational principle,fixed point theorems and parametric optimization problems

In this paper, we first establish some existence theorems of systems of generalized vector equilibrium problems. From these results, we obtain new variants of Ekeland’s variational principle in a Hausdorff t.v.s., a minimax theorem and minimization theorems. Some applications to the existence theorem of systems of semi-infinite problem, a variant of flower petal theorem and a generalization of Schauder’s fixed point theorem are also given.     

一类二阶非线性微分方程多点共振边值问题的可解性

讨论了一类二阶非线性微分方程多点共振边值问题,通过运用Mawhin连续定理,我们在一个较简单的条件下得到了问题的解的存在性结果.     

Coleman自同构群的投射极限

在这篇注记中，利用群的投射极限性质给出了有限可解群的Coleman自同构群的一个具体构造.作为应用，证明了二面体群的Coleman外自同构群或者是1或者是一个初等阿贝尔2-群.     

On Some Feasibility Conditions in MPEC

This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2].     

A nonlocal nonlinear diffusion equation in higher space dimensions

We study the initial-value problem for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation, in the whole RN, N?1, or in a bounded smooth domain with Neumann or Dirichlet boundary conditions. First, we prove the existence, uniqueness and the validity of a comparison principle for solutions of these problems. In RN we show that if initial data is bounded and compactly supported, then the solutions is compactly supported for all positive time t, this implies the existence of a free boundary. Concerning the Neumann problem, we prove that the asymptotic behavior of the solutions as t→∞, they converge to the mean value of the initial data. For the Dirichlet problem we prove that the asymptotic behavior of the solutions as t→∞, they converge to zero.     

An acceleration of Erlenkotter-Körkel’s algorithms for the uncapacitated facility location problem

This contribution is focused on an acceleration of branch and bound algorithms for the uncapacitated facility location problem. Our approach is based on the well-known Erlenkotters’ procedures and Körkels’ multi-ascent and multi-adjustment algorithms, which have proved to be the efficient tools for solving the large-sized instances of the uncapacitated facility location problem. These two original approaches were examined and a thorough analysis of their performance revealed how each particular procedure contributes to the computational time of the whole algorithms. These analyses helped us to focus our effort on the most frequent procedures. The unique contribution of this paper is a new dual ascent procedure. This procedure leads to considerable acceleration of the lower bound computation process and reduces the resulting computational time. To demonstrate more efficient performance of amended algorithms we present the results of extensive numerical experiments.     

线性互补问题的一类新的带参数价值函数的阻尼牛顿法

本文给出了线性互补问题LCP(q ,M)的一类新的带参数光滑价值函数 ,基此价值函数提出了一种阻尼牛顿类算法 ,并证明了当M为P 矩阵时 ,该算法全局收敛且有限步终止 .通过数值实验说明了该算法高效可靠 .与互补问题的磨光方程组中所采用的带参数价值函数不同 ,这里的参数最终并不趋向于零 ,而是趋向于被称作解的乘子向量 (与凸非线性极小极大问题的Lagrange乘子完全一致 ) ,这一思想是本文作者首次提出来的 ,同时本文中所采用的阻尼牛顿类方法也有其独到之处 ,在互补问题的研究中有进一步发展的潜力     

Robustness and nondegenerateness for linear complementarity problems

In this paper the main focus is on a stability concept for solutions of a linear complementarity problem. A solution of such a problem is robust if it is stable against slight perturbations of the data of the problem. Relations are investigated between the robustness, the nondegenerateness and the isolatedness of solutions. It turns out that an isolated nondegenerate solution is robust and also that a robust nondegenerate solution is isolated. Since the class of linear complementarity problems with only robust solutions or only nondegenerate solutions is not an open set, attention is paid to Garcia's classG _n of linear complementarity problems. The nondegenerate problems inG _n form an open set.     

研测动态问题的旋转孔径散斑照相法Ⅰ:双孔、四扇孔

本文提出一种研测动态问题的实验新方法——旋转孔径散斑照相法。该法设备简单,利用一个旋转孔径装置,能在一张散斑图上记录下物体动态变形的全过程,然后在全场波滤分析时把各瞬时的信息分离出来,可得任意时刻的瞬态位移场。转孔法能应用于振动和非周期性动态问题,并以三个实验证实其可行性。实验结果表明,散斑条纹清晰可靠,定量分析与其它方法所得结果一致。