低R.E度上D.R.E.度的非稠密性

本文用 O′′′优先损害方法证明了在 d.r e.度中任何低的递归可枚举度 l 之上存在一个非稠密区间,即存在 d.r.e.度 d,l相似文献   

低R.E度上D.R.E.度的非稠密性

本文用O(?)优先损害方法证明了d.r e.度中任何低的递归可枚举度ι之上存在一个非稠密区间,即存在d.r.e.度d,ι相似文献   

任何非递归r.e.度之下存在孤立d-r.e.度

证明了在任何非递归r.e.度之下都存在孤立d-r.s.度。     

ON CONE D.C. OPTIMIZATION AND CONJUGATE DUALITY

This paper derives first order necessary and sufficient conditions for unconstrained cone d.c. programming problems where the underlined space is partially ordered with respect to a cone. These conditions are given in terms of directional derivatives and subdifferentials of the component functions. Moreover, conjugate duality for cone d.c. optimization is discussed and weak duality theorem is proved in a more general partially ordered linear topological vector space (generalizing the results in [11]).     

d.r.e.度中钻石格的嵌入

本文证明了在d.r.e.度中,对任意高的递归可枚举度h,存在非零的d₁,d₂,使得d₁∪d₂=h,d₁∩d₂=0,即0,d₁,d₂,h构成钻石格.     

在d-r.e.度结构中真d-r.e.分支度的弱稠密性 *

证明了对任意r.e .度v相似文献   

I—ring which Satisfies A.D.C.C on Principal Left Ideals

Derndtl0n1AringRiscalledI-ring,ifasasemigroupRisgeneratedbyitsidemPOtentelements.Defhotl0n2AringRissaidtosatisfyalm0stdescending(0rascending)chaincondi-tionsonleftideals,ifforeverydescending(ascending)chainofleftideals0fR,I,nI2n...nI.Xi..-(I,GI2G...GI'g..-),thereexistsaPOsitiveintegerpsuchthatRPI=Ii(IiGR-'I,)foralli,whereR-'I,={ueRlR'u=IP}.By[5JitisknownthatAringRsatisfiesA.D.C.C(OTA.A.C,C)onleftidealsifandonlyifforeverydescending(0rascending)chalnOfleftidealsofR,I,nI2n-..n…     

格上点式p.q.度量的乘性

本文在可数多个分子格的乘积上构造了一个乘积点式p·q·度量函数,从而证明了点式p·q·度量分子格的可数积是可点式p·q·度量化的.     

关于强稠密语言与G.R.T-问题的一个等价陈述

在本文中,我们推广了[2]中相关对的概念,从而导出强稠密语言的概念,利用强稠密语言作为桥梁,我们给出了[1]中一个公开问题——G.R.T.-问题的一个等价陈述,同时也部分地回答了该问题.     

The Convergence of the Steepest Descent Algorithm for D.C.Optimization

Some properties of a class of quasi-differentiable functions(the difference of two finite convex functions) are considered in this paper.And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved.     

广义拟可微函数的微分

本文给出一种广义拟可微函数类,它是Demyanov与Rlubinov(1980)意义下拟可微函数的推广,通过凸集类对的空间的某些理论,建立了这类广义拟可微函数的微分学理论,包括加法运算、数乘运算、乘法运算、除法运算、极大值运算,极小值运算以及复合运算的微分公式和中值定理。这些结果为广义拟可微类函数优化研究提供了基本工具．     

一类特殊拟可微函数最优化问题的线性化方法

In this paper,we consider the problem of minimizing a particular class of quasi-differentiable functions:min{f(x)=max min fij(x)}.An algorithm for this problem is giver.At each iteration by solving quadratic programming subproblems to generate search directions,its convergence is proved in the sense of inf-stationary points.     

Calculus of Generalized Quasi－differentiable Functions Ⅰ：Some Results on the Space of Pairs of Convex－Set Collections

A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions.The space K1 is constructed by introducing a well-defined equivalence reation among pairs of collections of convex sets .Some important properties on the norm and operations is K1 are given.     

Fractional programming without differentiability

The notion of quasi-differentiability is examined and related to fractional programming. Necessary and sufficient conditions are given and various other properties of quasi-differentiable functions are discussed. Differentiability is not assumed.This research was partially supported by N.R.C. Grants A7751 and A7675.     

Calculus of Generalized Quasi-differentiable Functions I: Some Results on the Space of Pairs of Convex-Set Collections

A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.     

半层空间的函数刻画

本文探讨了半连续函数的一些性质,并利用半连续函数给出了对半层空间的几个等价刻画．     

A simplified conjugation scheme for lower semi-continuous functions

We present two generalized conjugation schemes for lower semi-continuous functions defined on a real Banach space whose norm is Fréchet differentiable off the origin, and sketch their applications to optimization duality theory. Both approaches are based upon a new characterization of lower semi-continuous functions as pointwise suprema of a special class of continuous functions.     

On second-order directional derivatives of value functions

Directional derivatives of value functions play an essential role in the sensitivity and stability analysis of parametric optimization problems, in studying bi-level and min–max problems, in quasi-differentiable calculus. Their calculation is studied in numerous works by A.V. Fiacco, V.F. Demyanov and A.M. Rubinov, R.T. Rockafellar, A. Shapiro, J.F. Bonnans, A.D. Ioffe, A. Auslender and R. Cominetti, and many other authors. This article is devoted to the existence of the second order directional derivatives of value functions in parametric problems with non-single-valued solutions. The main idea of the investigation approach is based on the development of the method of the first-order approximations by V.F. Demyanov and A.M. Rubinov.     

A Method for Converting a Class of Univariate Functions into d.c. Functions

D.c. functions are functions that can be expressed as the sum of a concave function and a convex function (or as the difference of two convex functions). In this paper, we extend the class of univariate functions that can be represented as d.c. functions. This expanded class is very broad including a large number of nonlinear and/or nonsmooth univariate functions. In addition, the procedure specifies explicitly the functional and numerical forms of the concave and convex functions that comprise the d.c. representation of the univariate functions. The procedure is illustrated using two numerical examples. Extensions of the conversion procedure for discontinuous univariate functions is also discussed.