极小扰动约束非线性规划的最优性条件

考虑当目标函数在约束条件下的最优值作扰动时，使各约束作极小扰动的非线性规划问题．文中引进了极小扰动约束规划的极小扰动有效解概念．利用把问题归为一个相应的多目标规划问题，给出了极小扰动约束有效解的最优性条件．     

一类非线性半向量二层规划问题的罚函数方法

本文研究了一类非线性-线性半向量二层规划问题的罚函数求解方法.对于该类半向量二层规划问题,首先基于下层问题的加权标量化方法和Karush-Kuhn-Tucker最优性条件,将其转化为一般的二层规划问题,并取下层问题的互补约束为罚项,构造出相应的罚问题;然后分析罚问题最优解的相关特征以及最优性条件,进而设计了相应的罚函数算法;最后以相关算例验证了罚函数算法的可行、有效性.     

关于一类二层规划问题的一阶最优性条件研究

本文针对一类具有特定结构的二层规划问题, 将下层问题用其KKT条件代替, 把二层规划问题转化成带有互补约束的单层优化问题.然后利用Fritz-John条件,在适当的条件下,得到了二层优化问题的一阶最优性条件.本文所给条件简单、容易验证,并且不同于[1]的条件.     

一类带概率互补约束的随机优化问题的最优性条件

主要讨论了一类带概率互补约束的随机优化问题的最优性条件.首先利用一类非线性互补(NCP)函数将概率互补约束转化成为一个通常的概率约束.然后,利用概率约束的相关理论结果,将其等价地转化成一个带不等式约束的优化问题.最后给出了这类问题的弱驻点和最优解的最优性条件.     

非可微二层凸规划的最优性条件

本文考虑的是构成函数为非可微凸函数的二层规划问题(NDBP),得到了下层极值函数和上层复合目标函数的方向导数和次微分的估计式,给出非可微二层凸规划(NDBP)最优解的几种最优性条件。     

较多约束多目标规划的最优性条件

本文研究较多约束多目标规划的最优性条件.借助于所给问题的较多约束集结构表示,定义了较多约束规划问题的较多约束Pareto有效解和较多约束Pareto弱有效解,给出较多约束Pareto有效解和较多约束Pareto弱有效解要满足的Fritz John条件和Kuhn-Tucker条件,最后给出在凸性条件下它的一些最优性充分条件.     

区间值函数的可微性及其在区间值规划中的应用

利用实值函数的全微分思想,讨论了区间值函数的可微性,建立了区间值函数的$D$-可微性的概念及其一些基本性质. 通过讨论无约束区间规划的最优性条件,给出了一类约束函数为实值函数的约束区间值规划问题取得最优解的必要条件. 同时给出了具有实值函数约束的凸区间值规划问题取得最优解的充分条件.     

一类广义半无限规划问题的一阶最优性条件

本文利用一个精确增广Lagrange函数研究了一类广义半无限极小极大规划问题。在一定的条件下将其转化为标准的半无限极小极大规划问题。研究了这两类问题的最优解和最优值之间的关系,利用这种关系和标准半无限极小极大规划问题的一阶最优性条件给出了这类广义半无限极小极大规划问题的一个新的一阶最优性条件。     

均衡约束数学规划的约束规格和最优性条件综述

约束规格在约束优化问题的最优性条件中起着重要的作用,介绍了近几年国际上关于均衡约束数学规划(简记为MPEC)的约束规格以及最优性条件的研究成果, 包括以下主要内容: (1) MPEC常用的约束规格(如线性无关约束规格 (MPEC-LICQ)、Mangasarian-Fromovitz约束规格 (MPEC-MFCQ)等)和新的约束规格(如恒秩约束规格、常数正线性相关约束规格等), 以及它们之间的关系; (2) MPEC常用的稳定点; (3) MPEC的最优性条件. 最后还对MPEC的约束规格和最优性条件的研究前景进行了探讨.     

模糊多目标半定规划的最优性条件

将模糊集理论应用到多目标半定规划中来,提出了有约束的模糊多目标半定规划模型,并首次给出了其最优有效解的定义.通过构造确定的隶属度函数,将以矩阵为决策变量的模糊多目标半定规划转化为一种目标函数的某些分量由约束函数决定的确定性多目标半定规划,并证明了前者最优有效解与后者有效解的一致性.在此基础之上,讨论了二者的最优性条件.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.