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1.
P. H. Sach 《Journal of Optimization Theory and Applications》2007,133(2):213-227
In this paper, we introduce the notion of (Benson) proper subgradient of a set-valued map and prove that, for some class of
nonconvex set-valued maps, a proper subgradient of the sum of two set-valued maps can be expressed as the sum of two proper
subgradients of these maps. This property is also established for weak subgradients. A result in Ref. [Lin, L.J.: J. Math.
Anal. Appl. 186, 30–51 (1994)], obtained under some convexity assumption, is included as a special case of the corresponding result of this paper.
The author thanks the anonymous referees for their valuable remarks. 相似文献
2.
本文利用集值映射弱次梯度的Morea-Rockafellar定理,在内部(锥)-凸性假设下,得到了集值映射关于Henig有效性的Morea-Rockafellar定理.其结论为:在内部(锥)-凸条件下,两个集值映射和的Henig有效次梯度可以表示成它们Henig有效次梯度的和. 相似文献
3.
Jianwen Peng Heung Wing Joseph Lee Xinmin Yang 《Journal of Mathematical Analysis and Applications》2005,302(2):441-449
In this paper, the notion of affinelike set-valued maps is introduced and some properties of these maps are presented. Then a new Hahn-Banach extension theorem with a K-convex set-valued map dominated by an affinelike set-valued map is obtained. 相似文献
4.
By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational
principle for a set-valued map. J. Optim. Theory Appl., 124, 187–206 (2005)] established a new version of Ekeland’s variational principle for set-valued maps, which is expressed by
the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement
of Ha’s version of set-valued Ekeland’s variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev
theorem. From the improved Ha’s version, we deduce a Caristi-Kirk’s fixed point theorem and a Takahashi’s nonconvex minimization
theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other. 相似文献
5.
The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.
This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science
Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002) 相似文献
6.
A new class of generalized convex set-valued functions, termed nearly-subconvexlike functions, is introduced. This class is a generalization of cone-subconvexlike maps, nearly-convexlike set-valued functions, and preinvex set-valued functions. Properties for the nearly-subconvexlike functions are derived and a theorem of the alternative is proved. A Lagrangian multiplier theorem is established and two scalarization theorems are obtained for vector optimization. 相似文献
7.
Weiping Zhang 《中国科学A辑(英文版)》1999,42(12):1279-1285
A mod 2 index theorem for the twisted Signature operator on 4
q
+ 1 dimensional manifolds is established. This result generalizes a result of Farber and Turaev, which was proved for the
case of orthogonal flat bundles, to arbitrary real vector bundles. It also provides an analytic interpretation of the sign
of the Poincare-Reidemeister scalar product defined by Farber and Turaev.
Project partially supported by the National Natural Science Foundation of China (Grant No. 19525102), the Fok Ying-Tung Foundation
and the Qiu Shi Foundation. 相似文献
8.
借助于相依上导数的概念,建立了锥次类凸集值映射的导数型择一性定理,并利用择一性定理获得了集值优化导数型的最优性必要条件和充分条件. 相似文献
9.
In this paper, by virtue of two intermediate derivative-like multifunctions, which depend on an element in the intermediate
space, some exact calculus rules are obtained for calculating the derivatives of the composition of two set-valued maps. Similar
rules are displayed for sums. Moreover, by using these calculus rules, the solution map of a parametrized variational inequality
and the variations of the feasible set of a parametrized mathematical programming problem are studied.
This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 10871216 and 60574073). 相似文献
10.
该文在赋范线性空间中对集值映射引入锥- Henig有效次梯度和锥- Henig有效次 微分的概念. 借助凸集分离定理证明了锥- Henig有效次微分的存在性, 并且建立了线性泛函为锥- Henig有效次梯度的充要条件. 最后, 对于一类参数 扰动集值优化问题讨论了其在Henig有效意义下的稳定性. 相似文献