A parametric view on the Mangasarian–Fromovitz constraint qualification

The growth of the multipliers, when the parameter approaches such a critical parameter, is characterized by a parametric constraint qualification which is introduced here. It is equivalent to a bound on the growth of the multipliers. Received May 8, 1995 / Revised version received February 12, 1998 Published online February 25, 1999     

外控弱周期电流约束下电极B-Z反应体系中的时间自组织

以经典BZ化学反应体系的三变量Oregonator模型及电极过程动力学为基础,提出了外控弱周期电极电流约束下电极BZ反应体系与体相BZ反应体系相互耦合的动力学模型.在体相处于稳定定态参数条件下,系统地研究了外控弱周期电流约束下电极BZ反应体系中的动力学行为,定量分析了电流慢变流型上的准定态稳定性及有利于出现极限环振荡区域.研究表明,与以前所报道的外控弱周期电位约束情况类似,在外控弱周期电流约束下电极BZ反应体系中的极限环振荡区域亦发生了蜕变,但体系对外控电流约束中的这种持续性之周期扰动的响应表现在两个方面:有利于出现极限环振荡区域的缩变及原非振荡区胁迫振荡的出现.     

Graph Coloring with Adaptive Evolutionary Algorithms

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EAs). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping Genetic Algorithm (GGA) on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping (GA) and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity.     

一类多维0-1背包问题的约束归并方法

提出一种新的关于多维背包(Multi-dimensions Knapsack Problem,MKP)的约束替代问题,MKP是NP-完全问题,称这种约束替代方法为不等式单约束平面生成法.叙述了单约束不等平面生成算法的基本思想,证明了此方法的一些性质及化简问题后所得到的新问题MKPS与原问题MKP的等价性.最后用实例证实了这种化简方法及其有效性。     

Boundary-value problems and the validity of the Post constraint in modern electromagnetism

When a (frequency-domain) boundary-value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the chosen material and a naïve application of the usual boundary conditions. It is shown here that the conflict vanishes when the boundary conditions are properly derived from the fundamental equations, and the validity of the Post constraint in modern macroscopic electromagnetism is thereby reaffirmed.     

Existences theorems of systems of vector quasi-equillibrium problems and mathematical programs with equilibrium constraint

In this paper, we introduce systems of vector quasi-equilibrium problems and prove the existence of their solutions. As applications of our results, we derive the existence theorems for solution of system of vector quasi-saddle point problem, the existences theorems of a solution of system of generalized quasi-minimax inequalities, the mathematical program with equilibrium constraint, semi-infinite and bilevel problems.     

New Relaxation Method for Mathematical Programs with Complementarity Constraints

In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising.     

奇异系统Hamilton正则方程的Mei对称性、Noether对称性和Lie对称性

研究奇异系统Hamilton正则方程的形式不变性即Mei对称性，给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明结果的应用. 关键词： 奇异系统 Hamilton正则方程 约束 对称性 守恒量     

Smooth positive extensions and nonlinear programming

We establish a smooth positive extension theorem: Given any closed subset of a finite-dimensional real Euclidean space, a function zero on the closed set can be extended to a function smooth on the whole space and positive on the complement of the closed set. This result was stimulated by nonlinear programming. We give several applications of this result to nonlinear programming.This paper is dedicated to the memory of Emily Sue Merkle Waite, Ph.D.The author wishes to thank W. Cunningham for suggesting the question about constraint qualifications, A. Karr for noticing the example of a Brownian motion sample path, R. Byrd and P. Hartman for discussions, and E. Waite for support and encouragement.     

二项分布下的一种贝叶斯可靠性验收试验方案

为了合理利用先验信息制定可靠性验收试验方案，以降低验收试验的费用，在进行可靠性定型试验的前提下，提出了一种先验信息加工方法，并根据生产与使用双方实际所关心的风险意义，制定了产品可靠性验收试验的一种贝叶斯方案。算例结果证实，该方案在保证了生产方与使用方利益的前提下，减少了试验量，降低了验收试验费用。说明所提出的先验信息利用方式是有效的。