共查询到20条相似文献,搜索用时 34 毫秒
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在赋范线性空间中借助切导数研究集值优化问题的严有效性.当目标函数和约束函数相对于同一向量函数为拟不变凸时,利用凸集分离定理给出了集值优化问题取得严有效元的Kuhn—Xhcker型最优陛必要条件.利用切导数的性质,用构造性方法得到了拟不变凸集值优化问题取得严有效元的充分条件. 相似文献
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In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature. 相似文献
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Ahmed Taa 《Journal of Global Optimization》2011,50(2):271-291
This paper investigates second-order optimality conditions for general multiobjective optimization problems with constraint
set-valued mappings and an arbitrary constraint set in Banach spaces. Without differentiability nor convexity on the data
and with a metric regularity assumption the second-order necessary conditions for weakly efficient solutions are given in
the primal form. Under some additional assumptions and with the help of Robinson -Ursescu open mapping theorem we obtain dual
second-order necessary optimality conditions in terms of Lagrange-Kuhn-Tucker multipliers. Also, the second-order sufficient
conditions are established whenever the decision space is finite dimensional. To this aim, we use the second-order projective
derivatives associated to the second-order projective tangent sets to the graphs introduced by Penot. From the results obtained
in this paper, we deduce and extend, in the special case some known results in scalar optimization and improve substantially
the few results known in vector case. 相似文献
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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. 相似文献
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首先定义了集值优化问题的m阶局部严格有效解并在赋范空间中研究了解的一些性质.在一定条件下,利用Dini导算子和支撑函数确立了m≥1阶严格有效解存在的充分必要条件. 相似文献
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On super efficiency in set-valued optimization 总被引:1,自引:0,他引:1
The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperation theorem, Kuhn-Tucker's, Lagrange's and saddle points optimality conditions, the necessary conditions are obtained for the set-valued optimization problem to attain its super efficient solutions. Also, the sufficient conditions for Kuhn-Tucker's, Lagrange's and saddle points optimality conditions are derived. 相似文献
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《Optimization》2012,61(5):921-954
ABSTRACTThe paper considers a class of vector optimization problems with cone constrained generalized equations. By virtue of advanced tools of variational analysis and generalized differentiation, a limiting normal cone of the graph of the normal cone constrained by the second-order cone is obtained. Based on the calmness condition, we derive an upper estimate of the coderivative for a composite set-valued mapping. The necessary optimality condition for the problem is established under the linear independent constraint qualification. As a special case, the obtained optimality condition is simplified with the help of strict complementarity relaxation conditions. The numerical results on different examples are given to illustrate the efficiency of the optimality conditions. 相似文献
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《Optimization》2012,61(12):2117-2137
ABSTRACTIn this paper, we study a vector optimization problem (VOP) with both inequality and equality constraints. We suppose that the functions involved are Fréchet differentiable and their Fréchet derivatives are continuous or stable at the point of study. By virtue of a second-order constraint qualification of Abadie type, we provide second-order Karush–Kuhn–Tucker type necessary optimality conditions for the VOP. Moreover, we also obtain second-order sufficient optimality conditions for a kind of strict local efficiency. Both the necessary conditions and the sufficient conditions are shown in equivalent pairs of primal and dual formulations by using theorems of the alternative for the VOP. 相似文献
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引进了一种二阶切导数,借助该切导数给出了变序结构集值优化问题取得局部弱非控点的二阶最优性必要条件.在某种特殊情况下,给出了一阶最优性条件.通过修正的Dubovitskij-Miljutin切锥导出的约束规格,给出了两个集值映射之和的二阶相依切导数的关系式,进一步得到目标函数与变锥函数的二阶相依切导数分开形式的最优性必要条件. 相似文献
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In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend the well-known Lagrange multiplier rule and the Kurcyusz–Robinson–Zowe regularity assumption to a constrained set-valued optimization problem in the second-order case. Simultaneously, we also establish some second-order Karush–Kuhn–Tucker necessary and sufficient optimality conditions for a set-valued optimization problem, whose feasible set is determined by a set-valued map, under a generalized second-order Kurcyusz–Robinson–Zowe regularity assumption. 相似文献
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Nguyen Le Hoang Anh Phan Quoc Khanh Le Thanh Tung 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7365-7379
We propose notions of higher-order outer and inner radial derivatives of set-valued maps and obtain main calculus rules. Some direct applications of these rules in proving optimality conditions for particular optimization problems are provided. Then we establish higher-order optimality necessary conditions and sufficient ones for a general set-valued vector optimization problem with inequality constraints. A number of examples illustrate both the calculus rules and the optimality conditions. In particular, they explain some advantages of our results over earlier existing ones and why we need higher-order radial derivatives. 相似文献
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In this paper, we consider higher-order Karush–Kuhn–Tucker optimality conditions in terms of radial derivatives for set-valued optimization with nonsolid ordering cones. First, we develop sum rules and chain rules in the form of equality for radial derivatives. Then, we investigate set-valued optimization including mixed constraints with both ordering cones in the objective and constraint spaces having possibly empty interior. We obtain necessary conditions for quasi-relative efficient solutions and sufficient conditions for Pareto efficient solutions. For the special case of weak efficient solutions, we receive even necessary and sufficient conditions. Our results are new or improve recent existing ones in the literature. 相似文献
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This paper deals with higher-order optimality conditions of set-valued optimization problems. By virtue of the higher-order derivatives introduced in (Aubin and Frankowska, Set-Valued Analysis, Birkhäuser, Boston, [1990]) higher-order necessary and sufficient optimality conditions are obtained for a set-valued optimization problem whose constraint condition is determined by a fixed set. Higher-order Fritz John type necessary and sufficient optimality conditions are also obtained for a set-valued optimization problem whose constraint condition is determined by a set-valued map. 相似文献
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Akhtar A. Khan 《Optimization》2013,62(6):743-758
In this article we give new second-order optimality conditions in set-valued optimization. We use the second-order asymptotic tangent cones to define second-order asymptotic derivatives and employ them to give the optimality conditions. We extend the well-known Dubovitskii–Milutin approach to set-valued optimization to express the optimality conditions given as an empty intersection of certain cones in the objective space. We also use some duality arguments to give new multiplier rules. By following the more commonly adopted direct approach, we also give optimality conditions in terms of a disjunction of certain cones in the image space. Several particular cases are discussed. 相似文献
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M. Durea 《Journal of Mathematical Analysis and Applications》2004,292(2):351-363
In this paper, we give two versions of Ky Fan's inequality for set-valued maps acting between normed vector spaces and we consider sufficient conditions to solve a variational inclusion problem concerning derivatives of set-valued maps. A selection result for set-valued maps between finite dimensional vector spaces and its contingent derivative is obtained as well; from this result we derive some conditions for the existence of a solution of a generalized variational inequality problem. 相似文献
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近似锥-次类凸集值优化的严有效性 总被引:16,自引:0,他引:16
在Hausdorff局部凸拓扑线性空间中考虑约束集值优化问题(VP)的严有效性.在近似锥-次类凸假设下,利用凸集分离定理,分别得到了Kuhn-Tucker型和Lagrange型最优性条件,建立了与(VP)等价的两种形式的无约束优化. 相似文献