具有多项式增长系数的随机延迟微分方程的整体解与矩估计

本文用Ito公式和Lyapunov函数法为具有多项式增长系数的随机延迟微分方程的整体解的存在和矩有界给出一个充分的条件.此条件适用于无限时滞的随机系统,对于有限时滞的随机系统也成立.     

处理退化问题的一类SQP算法

本文对不等式优化问题提出了一个修正的序列二次规划算法(SQP).该算法适用于退化问题一积极约束梯度线性相关且严格互补条件不成立,并且算法是可行的,具有整体收敛与超线性收敛性.     

半线性分布系统的最大原理(2)——时间最优问题

本文讨论在Banach空间上的非线性抽象Volterra型方程所决定的系统之时间最优问题。在目标集是连续变动的有界凸闭体条件下得到了最优控制的必要条件,证明了在文中的条件下最大原理成立,为进一步综合这类系统的时间最优问题提供了理论的出发点。 本文结果适用于一阶半线性发展系统、二阶及高阶半线性发展系统及由半线性泛函微分方程所决定的系统。     

充分条件与条件等式

若cosα=cosβ,则α=β。众所周知,这个命题是假命题。因为条件cosα=cosβ并不能充分保证结论a=β成立。如果要使结论α=β成立,则必须补充适当的条件。同上述相类似的问题往往容易被人们所忽视。本文将根据充分条件的定义,谈谈条件等式中的条件与结论间的依存关系,并举数例,以说明此问题,供同志们参考。定义如果A成立,则B也成立(简称“若A则B”或A B),就说A是B成立的充分条件。也就是说,有了条件A,就可以充分保证结论B一定成立。     

推广的积分第一中值定理的再改进

研究推广的积分第一中值定理成立的条件,弱化该定理成立应满足的基本要求,并进而得到被积函数连续性替代条件的相关推论.     

H lder不等式的推广及其应用

§1 引言文[1]叙述Holder不等式如下: 设α,β,¨,λ皆为正,且α+β+…+λ=1。则式中等号当且仅当(a),(b),…,(l)中存在一组与各组皆成比例时适用。 Jensen在上述条件不变的情况下,只将α+β+¨+λ≥1改变。不等式(1)仍然成立。本文类似上述情况,将条件改为0<α+β中…+λ<1时,不等式(1)仍然成立,即定理1 设α_i>0,α_(ij)>0(i=1,2.…,n;j=1,2,…,m),且.则     

债券价值对市场利率变化的敏感度

有关长期债券的价值对市场利率变化的敏感度高于短期债券的价值对市场利率变化的敏感度,本文给出了它成立的条件及它不成立的条件.     

基于Udwadia-Kalaba理论的Hamel嵌入法研究

Hamel嵌入法直接将约束嵌入到非约束运动的动能中去,从而避免使用Lagrange(拉格朗日)乘子.但这个简单、直观的方法却并不总是正确.Hamel认为这种方法可能导致错误的结果,然而他并没有给出Hamel嵌入法正确性的适用条件.在利用Udwadia Kalaba理论的基础上,提出了Hamel嵌入法成立的充要条件;指出了Rosenberg在Hamel嵌入法正确性研究中的不足,通过给出的具体算例可以看出,在完整约束下Hamel嵌入法可能不正确,而在非完整约束下也可能得出正确的结果;理论和实例分析表明,Hamel嵌入法是否成立除了与约束有关以外还与系统模型相关.     

适用于风向变化条件的毒气扩散模型研究

本文研究基于经典高斯扩散模式但适用于风向变化条件的毒气扩散模型。经典高斯扩散模式，例如高斯烟云模式和高斯烟团模式，成立的前提条件是在扩散过程中风向保持不变。但在实际应用中风向却常常是变化的。本文在经典高斯扩散模式的基础上引入坐标变换的数学方法，建立了一个能够应对风向变化条件的毒气扩散模型。该模型包括网格化预处理、高斯模式选择和坐标变化三个主要环节。文中详细阐述了模型的主要思想和核心算法。最后简要讨论了模型的程序设计和实际应用。     

活用均值不等式等号成立条件证难题

怎样证明不等式,大家常将关注落脚点放在不等式使用的技巧上,而对不等式的等号成立条件有所忽略．其实,如果注意合理使用不等式的等号成立条件,常常能帮助我们迅速找到一扇证明不等式难题的思路之门．     

Linear max-min programming

Theoretical aspects of the programming problem of maximizing the minimum value of a set of linear functionals subject to linear constraints are explored. Solution strategies are discussed and an optimality condition is developed. An algorithm is also presented.This research was partially supported by the Management Research Center of the University of Wisconsin—Milwaukee.     

Über werteannahme bei einer klasse von optlmalpromemen

If the minimal value of the objective function is not attained for certain optimization problems of the approximation type then the corresponding dual problem is not stable. This fact is based on the instability of the perturbated not correct stated problems with initial and boundary value conditions. The attainment of the minimal value is characterized by a condition which follows from the theory of stability of optimization problems.     

Optimization of a linear dynamic system with double terminal constraint on the trajectories

A linear-quadratic problem of optimal control with a double terminal constraint on the trajectories is considered. A new proof of the optimality criterion by means of the implicit fonctions theorem is given. The suggested condition ?-optimality of is formulated in the form of the maximum principle. The suggested optimization algorithm follows the Gabasov-Kirillova approach, which is based on the concept of so-called support control. The proposed algorithm is constructed without quantization of the continuous dynamic system and possesses a finishing procedure that gives the required accuracy in the construction of optimal control     

On the Pseudoconvexity of a Quadratic Fractional Function

In this paper we give a necessary and sufficient condition for the pseudoconvexity of a function f which is the ratio of a quadratic function over an affine function. The obtained results allow to suggest a simple algorithm to test the pseudoconvexity of f and also to characterize the pseudoconvexity of the sum of a linear and a linear fractional function.     

一类特殊线性双层规划的对偶规划

本文首先给出值型线性双层规划的等价形式 ,然后讨论了非增的值型线性双层规划的 Johri一般对偶规划 ,并且说明了其对偶间隙等于零 ,最后说明了它们最优解的关系     

A paradox in linear fractional transportation problems with mixed constraints

The present paper studies a paradox in Linear Fractional Transportation Problems with 'mixed constraints'. A sufficient condition for the existence of a paradox is established. Paradoxical range of flow is obtained for any flow in which the corresponding objective function value is less than that of the original Linear Fractional Transportation Problem with 'mixed constraints'     

The complementary unboundedness of dual feasible solution sets in convex programming

F.E. Clark has shown that if at least one of the feasible solution sets for a pair of dual linear programming problems is nonempty then at least one of them is both nonempty and unbounded. Subsequently, M. Avriel and A.C. Williams have obtained the same result in the more general context of (prototype posynomial) geometric programming. In this paper we show that the same result is actually false in the even more general context of convex programming — unless a certain regularity condition is satisfied.We also show that the regularity condition is so weak that it is automatically satisfied in linear programming (prototype posynomial) geometric programming, quadratic programming (with either linear or quadratic constraints),l _p -regression analysis, optimal location, roadway network analysis, and chemical equilibrium analysis. Moreover, we develop an equivalent regularity condition for each of the usual formulations of duality.Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR-73-2516.     

Minimal inequalities

We provide a characterization of minimal inequalities for bounded mixed integer programs, in terms of subadditive functions. The condition on the columns of the integer-constrained variables is analogous to that obtained earlier for the group problem, and we also determine the condition on the columns of the continuous variables.The research reported here was done at Carnegie-Mellon University.The report was prepared as part of the activities of the Management Sciences Research Group, Carnegie-Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with U.S. Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

Shadow prices in nonconvex mathematical programming

In this paper a definition is proposed for the concept of shadow prices in nonconvex programming. For a nonlinear program with equality and inequality constraints, existence of these prices and bounds for their possible values are obtained under the Mangasarian—Fromowitz regularity condition. Their exact values and some continuity properties are obtained under the more restrictive linear independence regularity condition. A definition of equilibrium prices is also proposed. Under convexity assumptions, all definitions and results coincide with those already known on this subject in convex programming.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-9273.