共查询到20条相似文献,搜索用时 0 毫秒
1.
In the paper, we show continuity of cone-convex set-valued maps by using nonconvex scalarization methods for sets. 相似文献
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We establish necessary and sufficient conditions for a stable Farkas’ lemma. We then derive necessary and sufficient conditions
for a stable duality of a cone-convex optimization problem, where strong duality holds for each linear perturbation of a given
convex objective function. As an application, we obtain stable duality results for convex semi-definite programs and convex
second-order cone programs.
The authors are grateful to the referees for their valuable suggestions and helpful detailed comments which have contributed
to the final preparation of the paper. The first author was supported by the Australian Research Council Linkage Program.
The second author was supported by the Basic Research Program of KOSEF (Grant No. R01-2006-000-10211-0). 相似文献
4.
Dual characterizations of the set containments with strict cone-convex inequalities in Banach spaces
We give characterizations of the containment of a convex set either in an arbitrary convex set or in a set described by reverse
cone-convex inequalities in Banach spaces. The convex sets under consideration are the solution sets of an arbitrary number
of cone-convex inequalities, which can be either weak or strict inequalities. These characterizations provide ways of verifying
the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated
systems. Particular cases of dual characterizations of set containments have played key roles in solving large scale knowledge-based
data classification problems, where they are used to describe the containments as inequality constraints in optimization problems.
The concept of evenly convex set is used to derive the dual conditions, characterizing the set containments.
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《Optimization》2012,61(2):197-223
We consider functions with values in the power set of a pre-ordered, separated locally convex space with closed convex images. To each such function, a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre–Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. To the set-valued conjugate, a full calculus is provided, including a biconjugation theorem, a chain rule and weak and strong duality results of the Fenchel–Rockafellar type. 相似文献
8.
We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we
give some consequences. 相似文献
9.
《Indagationes Mathematicae (Proceedings)》1982,85(3):303-309
A certain broad class of finite-meromorphic operator functions is characterized by the existence of local representations as the product or sum of two operator functions with special properties. Similar global decompositions are also obtained. The class studied includes, for example, all finite-meromorphic operator functions whose values are semi-Fredholm operators. 相似文献
10.
M. Fabian G. Godefroy V. Zizler 《Journal of Mathematical Analysis and Applications》2004,297(2):419-455
We give characterizations of weakly compactly generated spaces, their subspaces, Vašák spaces, weakly Lindelöf determined spaces as well as several other classes of Banach spaces related to uniform Gâteaux smoothness, in terms of the presence of a total subset of the space with some additional properties. In addition, we describe geometrically, when possible, these classes by means of suitable smoothness or rotundity of the norm. As a consequence, we get new, functional analytic proofs of several theorems on (uniform) Eberlein, Gul'ko and Talagrand compacta. 相似文献
11.
Attila Gilányi Katarzyna Troczka-Pawelec 《Journal of Mathematical Analysis and Applications》2011,382(2):814-821
Related to the theory of convex and subadditive functions, we investigate weakly subquadratic mappings, that is, solutions of the inequality
12.
S. Schaible 《Journal of Optimization Theory and Applications》1977,21(1):15-26
The paper deals with strictly pseudoconvex quadratic functions on open convex sets. It presents second-order conditions in terms of an extended Hessian and in terms of bordered determinants. All of the conditions are both necessary and sufficient.The author wishes to thank Professor M. Avriel, visiting Stanford University, for helpful discussions. He is also grateful to Professor R. W. Cottle, Stanford University, for his suggestions. 相似文献
13.
Some characterizations of strongly preinvex functions 总被引:1,自引:0,他引:1
Muhammad Aslam Noor Khalida Inayat Noor 《Journal of Mathematical Analysis and Applications》2006,316(2):697-706
In this paper, a new class of generalized convex function is introduced, which is called the strongly α-preinvex function. We study some properties of strongly α-preinvex function. In particular, we establish the equivalence among the strongly α-preinvex functions, strongly α-invex functions and strongly αη-monotonicity under some suitable conditions. As special cases, one can obtain several new and previously known results for α-preinvex (invex) functions. 相似文献
14.
Second order characterizations for (strictly) pseudoconvex functions are derived in terms of extended Hessians and bordered determinants. Additional results are presented for quadratic functions. 相似文献
15.
E. M. J. Bertin W. Hengartner R. Theodorescu 《Probability Theory and Related Fields》1981,57(3):327-338
Let F be a distribution function and let Q
F(l)=0 for l<0 and Q
F(l)= sup {F(x+l)–F(x): x} for l0 be its Lévy concentration function. This paper has two purposes: to give a characterization of unimodal distribution functions (Theorem 3.5) and a representation theorem for the class of unimodal distribution functions (Theorem 6.2), both in terms of their Lévy concentration functions.Work supported by the Natural Sciences and Engineering Research Council Canada Grants A-7339 and A-7223, by the Québec Action Concertée Grant ER-1023, and by the Deutsche Forschungsgemeinschaft 相似文献
16.
Generalized second-order characterizations of convex functions 总被引:1,自引:0,他引:1
X. Q. Yang 《Journal of Optimization Theory and Applications》1994,82(1):173-180
We introduce a second-order upper Dini-directional derivative and obtain a second-order characterization for a continuously Gâteaux differentiable function to be a convex function.This research was done under the supervision of Dr. V. Jeyakumar whose helpful guidance and valuable suggestions are much appreciated. The author is thankful to the referee for providing a simplication of the original proof of Theorem 2.1. 相似文献
17.
《Operations Research Letters》1987,6(6):297-300
A continuum structure function is a non-decreasing mapping from the unit hypercube to the unit interval. Axiomatic characterizations of the continuum structure functions based on the Barlow-Wu and Natvig multistate structure functions are derived. 相似文献
18.
We provide some characterizations for SOC-monotone and SOC-convex functions by using differential analysis. From these characterizations,
we particularly obtain that a continuously differentiable function defined in an open interval is SOC-monotone (SOC-convex)
of order n ≥ 3 if and only if it is 2-matrix monotone (matrix convex), and furthermore, such a function is also SOC-monotone (SOC-convex)
of order n ≤ 2 if it is 2-matrix monotone (matrix convex). In addition, we also prove that Conjecture 4.2 proposed in Chen (Optimization
55:363–385, 2006) does not hold in general. Some examples are included to illustrate that these characterizations open convenient
ways to verify the SOC-monotonicity and the SOC-convexity of a continuously differentiable function defined on an open interval,
which are often involved in the solution methods of the convex second-order cone optimization. 相似文献
19.
A functionf(X
1,X
2, ...,X
n
) is said to betth-order correlation-immune if the random variableZ=f(X
1,X
2,...,X
n
) is independent of every set oft random variables chosen from the independent equiprobable random variablesX
1,X
2,...,X
n
. Additionally, if all possible outputs are equally likely, thenf is called at-resilient function. In this paper, we provide three different characterizations oft th-order correlation immune functions and resilient functions where the random variable is overGF (q). The first is in terms of the structure of a certain associated matrix. The second characterization involves Fourier transforms. The third characterization establishes the equivalence of resilient functions and large sets of orthogonal arrays. 相似文献
20.
Journal d'Analyse Mathématique - 相似文献