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在Goetschel-Voxman所定义的序关系下,首先讨论了模糊值函数的凸性,得到了凸模糊值函数的若干充分条件,并证明了凸模糊值函数的Jensen不等式;其次,讨论了凸模糊值函数的次可微性,给出了次微分的若干重要性质,并得到了次可微条件下取得最优解的充分必要条件以及若干个次可微的充分条件. 相似文献
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下半连续函数的Proximal—次微分与广义中值定理 总被引:5,自引:3,他引:2
郭兴明 《数学物理学报(A辑)》1998,18(3):324-329
该文对定义在Hilbert空间E上的一般下半连续函数证明了如[9]中形式的逼近中值定理在Proximal-次微分意义下也成立.若E=[a,b]R,则得到了不等式形式的中值定理.作为应用给出了函数凸性、Lipschitz性质及常数性质的Proximal-次微分刻划. 相似文献
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本文研究具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性.假设多值非线性和脉冲函数满足由非紧性测度表示的正则性条件,利用非紧性测度理论和多值凝聚不动点定理,得到这类微分包含的可控性的充分条件. 相似文献
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本文使用Clarke次微分分析了定义在Banach空间的局部Lipschitz连续的伪线性函数的性质,并且考虑了伪线性规划解集的性质. 相似文献
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Katya Scheinberg Donald Goldfarb Xi Bai 《Foundations of Computational Mathematics》2014,14(3):389-417
We propose new versions of accelerated first-order methods for convex composite optimization, where the prox parameter is allowed to increase from one iteration to the next. In particular, we show that a full backtracking strategy can be used within the FISTA and FALM algorithms while preserving their worst-case iteration complexities of $O(\sqrt{L(f)/\epsilon })$ . In the original versions of FISTA and FALM the prox parameter value on each iteration must be bounded from above by its value on prior iterations. The complexity of the algorithm then depends on the smallest value of the prox parameter encountered by the algorithm. The theoretical implications of using full backtracking in the framework of accelerated first-order and alternating linearization methods allow for better complexity estimates that depend on the “average” prox parameter value. Moreover, we show that in the case of compressed sensing problem and Lasso, the additional cost of the new backtracking strategy is negligible compared to the cost of the original FISTA iteration. Our computational results show the benefit of the new algorithm. 相似文献
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In this paper we review some of the recently introduced hypertopologies on collections of nonempty closed subsets of a metrizable space in the context of continuity properties of the prox map and the restricted center map. We identify here suitable families A, B of nonempty closed sets equipped with natural topologies, as coordinate spaces for the gap functional and the restricted radius functional, with a view to explore bivariate continuity of these functionals. This leads us to sharpenings of many known results as well as to some new results for upper semicontinuity of the prox map and the restricted center map. This, in turn, also leads us to improvements of certain best approximation results for convex-valued multifunctions and fixed point theorems for such multifunctions. 相似文献
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具有拟理想正则*-断面的正则半群 总被引:4,自引:1,他引:3
本文提出了具有正则*-断面正则半群的概念,所给出的例子表明具有拟理想正则*-断面的正则半群类真包含了具有拟理想逆断面的正则半群类和正则*-半群类;最后刻画了具有拟理想正则*-断面的正则半群的结构. 相似文献
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正则函数是Clifford分析中的一类重要函数,加权正则函数是正则函数的进一步发展,也是一类重要的函数,因此具有一定的研究意义.在正则函数的研究基础上,并利用加权正则函数自身的性质,讨论了加权正则函数的平均值定理,最大模原理,Weierstrass定理以及一些其它推论. 相似文献
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Some problems in the theory of R-closed spaces are solved by showing that every regular space can be embedded in a minimal regular space and there is an R-closed space with no coarser minimal regular topology. A class of spaces is found so that when fed into the Jone's machinery for producing non-Tychonoff, regular spaces, the output is non-tychonoff R-closed and minimal regular spaces. Also, an example of a strongly minimal regular space that is not locally R-closed is given. 相似文献
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关于Fuzzy完全正则半群 总被引:3,自引:3,他引:0
本文先引入Fuzzy左(Fuzzy右)正则半群的概念,进而讨论Fuzzy左(Fuzzy右)正则半群以及Fuzzy完全正则半群中Fuzzy理想的一些代数性质。 相似文献
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SUN Xiangrong HE Wei School of Mathematics Computer Science Nanjing Normal University Nanjing China. 《数学年刊A辑(中文版)》2007,(6)
利用Locale中的完全正则元和零维元构造性地给出了任意Locale的完全正则反射以及零维反射的描述,并且对于满足‘(?)’关系插入性的Locale,特别地,对正规Locale,证明了全体正则元构成的Locale是其正则反射.进而,利用平稳(flat)子Locale的扩张引理给出了Locale的紧完全正则反射,紧零维反射以及紧正则反射的构造性描述. 相似文献
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Till Plewe 《Applied Categorical Structures》2000,8(1-2):17-44
We consider regular epimorphisms in the category Loc of locales. Closed surjections with subfit domain are regular epimorphisms. However, there exists a closed surjection which is the composite of two regular epimorphisms without being regular epic itself. This example answers both of the following questions in the negative: Y. Li"s question of whether weak quotient maps are necessarily regular epimorphisms, and P. Johnstone"s related question of whether regular epimorphisms compose. It follows that not all extremal epimorphisms in Loc are regular. The weak quotient maps of Y. Li and the equationally closed subframes of A. Pultr and A. Tozzi are shown to be dual notions. We also give a new characterization of regular epimorphisms in Loc. 相似文献
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本文首先在一般L-fuzzy拓扑空间中引入了包含式正则分离性的概念.其次将包含式正则分离性与点式正则分离性及正则分离性作了比较,讨论了它们之间的相互蕴含关系.最后说明了包含式正则分离性与包含式正规分离性及包含式完全正则分离性之间的协调性. 相似文献