集值优化问题的Benson真有效解的广义导数型最优性条件

引进了集值映射关于锥的Clarke切导数, Adjacent切导数与Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义导数型最优性条件．     

集值优化问题的Benson真有效解的广义最优性条件

引进了关于集值映射的(1,α)-阶Clarke导数,(1,α)-阶邻接导数,(1,α)-阶伴随导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义导数型Kuhn-Tucker最优性条件。     

Benson真有效解意义下集值优化问题的最优性条件

引进了集值映射关于锥的(1,α)-阶Clarke切导数,(1,α)-阶Adjacent切导数,(1,α)-阶Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义Kuhn-Tucker最优性条件．     

Benson真有效意义下向量集值优化的广义Fritz John条件

引入了一种有关集值映射的切导数和强、弱*伪凸的概念。借助凸集分离定理及锥分离定理建立了Benson真有效意义下向量集值优化导数型的FritzJohn最优性条件,并对条件的充分性进行了讨论。当特殊到单值映射时这些最优性条件与经典的结果完全吻合。     

Benson真有效意义下集值优化的广义最优性条件

本文引入了关于集值映射的α-阶Clarke切导数、α-阶邻接切导数及α-阶 伴随切导数的概念,借此建立了约束向量集值优化Benson真有效解导数型的Kuhn- Tucker条件.     

向量集值优化超有效解的对偶问题

借助于Contingent切锥和集值映射的上图而引入的有关集值映射的Contingent切导数，对约束集值优化问题的超有效解建立了最优性Kuhn Tucker必要及充分性条件,借此建立了向量集值优化超有效解的Wolfe型和Mond Weir型对偶定理.     

集值优化问题在有效意义下的最优性条件

本文在赋范空间中,讨论集值优化问题的有效元导数型最优性条件.当目标映射和约束映射的下方向导数存在时,在近似锥次类凸假设下利用有效点的性质和凸集分离定理得到了集值优化问题有效元导数型Kuhn-Thcker必要条件,在可微Г-拟凸性的假设下得到了Kuhn-Tucker最优性充分条件;此外利用集值映射沿弱方向锥的导数的特性给出了有效解最优性的另一种刻画.     

方向导数和广义锥-预不变凸集值优化问题

讨论拓扑向量空间中无约束集值优化问题的最优性条件问题.利用集值映射的Dini方向导数,在广义锥-预不变凸性条件下,建立了集值优化问题关于弱极小元和强极小元的最优性充分必要条件.     

一类新的二阶组合切导数及其应用

引进了一种新的切锥,讨论它与相依切锥的关系.借助这种新的切锥引进了一类新的二阶组合切导数,并讨论了它与其他二阶切导数的关系.利用这类新的二阶组合切导数,建立了集值优化分别取得Henig有效元和全局有效元的最优性必要条件.     

集值优化问题的高阶最优性条件(借助Studniarski导数)(英文)

本文研究的是约束集值优化问题的高价最优性条件.首先通过借助集值映射的Stud-niarski导数和严格局部有效性,讨论了集值优化问题的高阶必要条件和充分条件.对于充分条件,初始空间必须是有限维的.其次在初始空间和目标空间是有限维的以及集值映射是m阶稳定的条件下,也得到了此约束集值优化问题的高阶最优性条件.     

Benson 真有效意义下向量优化的最优性条件

对向量值映射引入了Clarke切导数,A djacent切导数及Contingent导数的概念,讨论了它们的性质,并用其建立了束向量优化有效解在Benson真有效意义下的Fritz John及Kunh-Tucker条件。     

Weak Clarke epiderivative in set-valued optimization

A new notion of weak Clarke epiderivative for a set-valued map is introduced using the concept of Clarke tangent cone. The existence, characterization and properties of weak Clarke epiderivative are then studied. Finally optimality criteria are established for a constrained set-valued optimization problem in terms of weak Clarke epiderivative.     

No Gap Second-Order Optimality Conditions for Circular Conic Programs

In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end.     

Acta Mathematica Scientia

1IntroductionLetfibeaboundeddomainOfR"withsmoothboundaryoff,KCL'(fl)xL'(fl)beasubsetdefinedasfollows:K={(yi,yi)EL'(fl)xL'(fl);yi(x) p(yl(x))30,a.e.infi},(1)withwhichisamaximalmonotonegraphonRxR.Whereaisapositiveconstant.Ourmainproblemisasfollows:(O)MinimizeL(y,u)={'[g(y(t)) h(u(t))]at,overallpairssubjecttotheconditionsOurbasichypothesesaboutgandharethefollowing:(H)Bothgandh:L'(fl)~(--co, co]arelowersendcontinuous,convexsproperfunctionals,withg(y)相似文献   

Isotone tangent cones and nonsmooth optimization

A simple but quite general method of formulating necessary optimality conditions for an abstract mathematical program is presented. This method centers around tangent cones which are isotone with respect to inclusion. The optimality conditions derived by this method generalize standard necessary conditions of differentiate, convex, and nonsmooth mathematical programming.