带误差项的下降算法的收敛性

本文考虑了Solodov和Svaiter提出的带误差项的下降算法的收敛性．其重要特征是在收敛性的证明过程中没有应用梯度函数的Hlder连续性．因此,我们在较弱的条件下得到了该算法的收敛性结果．     

一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型的定性分析

考虑了一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型．运用离散动力系统的频闪映射,获得了一个‘微生物灭绝’周期解,进一步获得了该周期解全局吸引的充分条件．运用脉冲时滞泛函微分方程新的计算技巧,证明了系统在适当的条件下是持久的,结论还表明该时滞是“有害”时滞．     

关于EV线性回归模型中的广义最小二乘估计

本文考虑EV（errors-in-variables）线性模型．在一般的条件下证明了广义最小二乘估计的强收敛和渐近正态性，然后在小样本意义下给出了模拟结果．     

环与剩余类环的同调维数

Ｓａｎｄｏｍｉｅｒｓｋｉ Ｆ．Ｌ,Ｓｍａｌｌ Ｌ．Ｗ,和 Ｆｉｅｌｄｓ Ｋ．Ｌ．［１－２］在“幂零”条件下研究了环与约化环的同调维数．然而对一些环（如交换 Ｖｏｎ Ｎｅｕｍａｎｎ正则环）,“幂零’的条件是不成立的．因此,在本文中我们考虑非“幂零”条件下（如Ｒ（Ｒ／Ｉ）（（Ｒ／Ｉ）Ｒ）是Ｒ－投身的或Ｒ（Ｒ／Ｉ）Ｒ是Ｒ－平坦的）,环与约化环的同调维数．     

垃圾填埋气体渗流过程中压力分布的滑脱解

考虑气体滑脱效应条件下,建立了垃圾填埋场气体渗流的数学模型．采用摄动法及积分变换法对模型进行解析求解,定量研究填埋气体的压力分布特征,并结合监测数据对模型参数与模型可靠性进行灵敏度分析和验证．结果表明:滑脱效应对气体渗流有较大影响,考虑滑脱效应条件的气体压力小于未考虑滑脱效应条件的气体压力,且得到的滑脱解与实测数值吻合较好．因此,研究填埋气体渗流时不能忽略滑脱效应．这不仅对于填埋场释放气体控制系统的设计和管理提供理论依据,而且可为低渗透油气藏工程开发过程中试井数据的确定提供科学的技术支持．     

一类SARS传染病自治动力系统的稳定性分析

在K-M传染病模型的基础上,进一步考虑易感人群的密度制约以及患病者类的死亡与治愈率等因素,建立了描述SARS传染病的一个新的动力学模型,分析了该模型平衡点的稳定性态．证明了疾病消除平衡点在一定条件下是全局渐进稳定的,而地方病平衡点不是渐近稳定的．得到了该传染病系统在适当条件下为永久持续生存的结果．     

一类半导体方程组弱解的存在性

考虑一类半导体方程组的混合初边值问题．在边值函数非负的条件下。证明了整体弱解的存在性．     

用Adomian分解法求解分数阻尼梁的解析解

利用Adomian分解法, 得到了由任意阶分数微分描述的具有阻尼特性的黏弹性连续梁的解析解．解中包含了任意的初始条件和零输入．为了更明确的分析, 假定初始条件是奇次的,输入受力是针对某种特定梁的特殊过程．分别考虑了两种简单情况下梁的响应:阶跃激励和脉冲激励．然后在系统的不同组参数条件下绘制了梁的位移图,并且讨论了梁在不同微分阶数下响应情况．     

二系悬挂条件下的车-路垂向耦合系统的动力模型

在车辆的走行过程中,上部与下部是相互作用和影响的．因此,轨道交通问题实际上就是线路下部结构和车辆系统的体系匹配问题．在一系悬挂条件下的车-路系统耦合动力分析模型基础上,考虑了包含转向架在内的车辆的实际构成和轨下基础包括路基和地基的参振特性,利用轨道维护标准模拟行走不平顺激励,通过位移相容条件,从理论上研究车辆-轨道-路基体系的动力相互作用,建立了二系悬挂条件下的车辆-轨道-路基系统的垂向动力分析模型．为高速铁路路基的动力特性分析和设计提供参考．     

高阶中立型微分方程正解的存在性

考虑ｎ阶中立型微分方程其中ｎ≥１是奇数．在对ｆ较弱的限制条件下，本文获得了方程（＊）当ｐ≠─１时存在正解的充分条件以及当ｐ＝－１时存在有界正解的充分必要条件．本文结果部分地回答了文献［１］中的公开问题．     

Optimality conditions for nonconvex semidefinite programming

This paper concerns nonlinear semidefinite programming problems for which no convexity assumptions can be made. We derive first- and second-order optimality conditions analogous to those for nonlinear programming. Using techniques similar to those used in nonlinear programming, we extend existing theory to cover situations where the constraint matrix is structurally sparse. The discussion covers the case when strict complementarity does not hold. The regularity conditions used are consistent with those of nonlinear programming in the sense that the conventional optimality conditions for nonlinear programming are obtained when the constraint matrix is diagonal. Received: May 15, 1998 / Accepted: April 12, 2000?Published online May 12, 2000     

A unified treatment of fuzzy set theory and Boolean-valued set theory—Fuzzy set structures and normal fuzzy set structures

This is Part I of a two-part paper; the purpose of this two-part paper is (a) to develop new concepts and techniques in the theory of infinite-dimensional programming, and (b) to obtain fruitful applications in continuous time programming. Part I deals with the development of continuous time analogues to those concepts which are the cornerstones of finite-dimensional programming theory. Specifically, a constraint qualification analogous to that found in finite-dimensional programming and a continuous time version of Farkas' theorem are developed. The latter result, stated in terms of convex and polar cones, is then employed in conjunction with the newly-developed constraint qualification to establish necessary conditions and a duality theory for a class of nonlinear continuous time programming problems. This approach to duality permits the imposition of assumptions that are less stringent than those needed for duality in previous formulations of the nonlinear problem.     

灰色双矩阵博弈模型及其均衡解

在支付矩阵和约束条件都是灰色的情况下,给出灰双矩阵博弈的一般形式,并且定义了灰双矩阵博弈的均衡解,证明灰双矩阵博弈的均衡解可由求解一个非线性规划问题得到.     

A class of nonlinear Lagrangians for nonconvex second order cone programming

This paper focuses on the study of a class of nonlinear Lagrangians for solving nonconvex second order cone programming problems. The nonlinear Lagrangians are generated by Löwner operators associated with convex real-valued functions. A set of conditions on the convex real-valued functions are proposed to guarantee the convergence of nonlinear Lagrangian algorithms. These conditions are satisfied by well-known nonlinear Lagrangians appeared in the literature. The convergence properties for the nonlinear Lagrange method are discussed when subproblems are assumed to be solved exactly and inexactly, respectively. The convergence theorems show that, under the second order sufficient conditions with sigma-term and the strict constraint nondegeneracy condition, the algorithm based on any of nonlinear Lagrangians in the class is locally convergent when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Compared to the analysis in nonlinear Lagrangian methods for nonlinear programming, we have to deal with the sigma term in the convergence analysis. Finally, we report numerical results by using modified Frisch’s function, modified Carroll’s function and the Log-Sigmoid function.     

Superlinearly convergent approximate Newton methods for LC1 optimization problems

In the literature, the proof of superlinear convergence of approximate Newton or SQP methods for solving nonlinear programming problems requires twice smoothness of the objective and constraint functions. Sometimes, the second-order derivatives of those functions are required to be Lipschitzian. In this paper, we present approximate Newton or SQP methods for solving nonlinear programming problems whose objective and constraint functions have locally Lipschitzian derivatives, and establishQ-superlinear convergence of these methods under the assumption that these derivatives are semismooth. This assumption is weaker than the second-order differentiability. The extended linear-quadratic programming problem in the fully quadratic case is an example of nonlinear programming problems whose objective functions have semismooth but not smooth derivatives.This work is supported by the Australian Research Council.This paper is dedicated to Professor O.L. Mangasarian on the occasion of his 60th birthday.     

New Constraint Qualifications and Optimality Conditions for Second Order Cone Programs

We introduce three new constraint qualifications for nonlinear second order cone programming problems that we call constant rank constraint qualification, relaxed constant rank constraint qualification and constant rank of the subspace component condition. Our development is inspired by the corresponding constraint qualifications for nonlinear programming problems. We provide proofs and examples that show the relations of the three new constraint qualifications with other known constraint qualifications. In particular, the new constraint qualifications neither imply nor are implied by Robinson’s constraint qualification, but they are stronger than Abadie’s constraint qualification. First order necessary optimality conditions are shown to hold under the three new constraint qualifications, whereas the second order necessary conditions hold for two of them, the constant rank constraint qualification and the relaxed constant rank constraint qualification.

     

Second-order necessary conditions of the Kuhn-Tucker type under new constraint qualifications

We are concerned with a nonlinear programming problem with equality and inequality constraints. We shall give second-order necessary conditions of the Kuhn-Tucker type and prove that the conditions hold under new constraint qualifications. The constraint qualifications are weaker than those given by Ben-Tal (Ref. 1).The author would like to thank Professor N. Furukawa and the referees for their many valuable comments and helpful suggestions.     

Lower-Order Penalization Approach to Nonlinear Semidefinite Programming

In this paper, we reformulate a nonlinear semidefinite programming problem into an optimization problem with a matrix equality constraint. We apply a lower-order penalization approach to the reformulated problem. Necessary and sufficient conditions that guarantee the global (local) exactness of the lower-order penalty functions are derived. Convergence results of the optimal values and optimal solutions of the penalty problems to those of the original semidefinite program are established. Since the penalty functions may not be smooth or even locally Lipschitz, we invoke the Ekeland variational principle to derive necessary optimality conditions for the penalty problems. Under certain conditions, we show that any limit point of a sequence of stationary points of the penalty problems is a KKT stationary point of the original semidefinite program. Communicated by Y. Zhang This work was supported by a Postdoctoral Fellowship of Hong Kong Polytechnic University and by the Research Grants Council of Hong Kong.     

Threshold Boolean form for joint probabilistic constraints with random technology matrix

We develop a new modeling and solution method for stochastic programming problems that include a joint probabilistic constraint in which the multirow random technology matrix is discretely distributed. We binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined Boolean function (pdBf) representing the probabilistic constraint. We then construct a tight threshold Boolean minorant for the pdBf. Any separating structure of the tight threshold Boolean minorant defines sufficient conditions for the satisfaction of the probabilistic constraint and takes the form of a system of linear constraints. We use the separating structure to derive three new deterministic formulations for the studied stochastic problem, and we derive a set of strengthening valid inequalities. A crucial feature of the new integer formulations is that the number of integer variables does not depend on the number of scenarios used to represent uncertainty. The computational study, based on instances of the stochastic capital rationing problem, shows that the mixed-integer linear programming formulations are orders of magnitude faster to solve than the mixed-integer nonlinear programming formulation. The method integrating the valid inequalities in a branch-and-bound algorithm has the best performance.