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M. SEMU 《数学年刊B辑(英文版)》2003,24(4):521-528
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]). 相似文献
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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. 相似文献
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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… 相似文献
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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. 相似文献
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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. 相似文献
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SONG Chun-ling~ 《数学季刊》2007,(1)
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. 相似文献
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姚静 《高等学校计算数学学报》2002,24(2):135-144
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. 相似文献
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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. 相似文献
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J. M. Borwein 《Mathematical Programming》1976,11(1):283-290
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. 相似文献
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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. 相似文献
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Leonardo M. Elias 《Optimization》2016,65(4):751-763
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. 相似文献
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《Optimization》2012,61(2):389-407
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. 相似文献
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Bruce W. Lamar 《Journal of Global Optimization》1999,15(1):55-71
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. 相似文献