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多目标优化问题Proximal真有效解的最优性条件 总被引:1,自引:1,他引:0
在广义凸性假设下,给出了集合proximal真有效点的线性标量化,并在此基础上证明了它与Benson真有效点和Borwein真有效点的等价性.将这些结果应用到多目标优化问题上,得到proximal真有效解的最优性条件.最后,利用proximal次微分,得到了proximal真有效解的模糊型最优性条件. 相似文献
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本文研究一类非光滑向量均衡问题(Vector Equilibrium Problem)(VEP)关于近似拟全局真有效解的最优性条件.首先,利用凸集的拟相对内部型分离定理和Clarke次微分的性质,得到了问题(VEP)关于近似拟全局真有效解的最优性必要条件.其次,引入近似伪拟凸函数的概念,并给出具体实例验证其存在性,且在该凸性假设下建立了问题(VEP)关于近似拟全局真有效解的充分条件.最后,利用Tammer函数以及构建满足一定性质的非线性泛函,得到了问题(VEP)近似拟全局真有效解的标量化定理. 相似文献
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群体多目标决策联合有效解类的不变凸充分条件 总被引:2,自引:0,他引:2
对于群体多目标决策问题,文[1]引进它的联合有效解类的概念,并给出这类解的最优性必要条件,在对于问题的目标函数和约束函数附加凸性的条件下,文[2]又给出了联合有效解类的最优性充分条件,本文进一步在目标函数和约束函数具不变凸和不变广义 凸的情况下,分别给出了联合有效解类的若干最优性充分条件。 相似文献
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群体多目标决策联合有效解类的几个最优性充分条件 总被引:6,自引:1,他引:5
对于群体多目标决策问题,文献[1]利用供选方案的有效数引进一类基本的联合有效解概念,并且给出了此类解要满足的最优性必要条件。本文在一定凸性要求下,建立了群体多目标决策问题联合有效解类的若干最优性充分条件。 相似文献
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华盛信余国林韩文艳孔翔宇 《数学物理学报(A辑)》2022,(2):365-378
该文研究一类约束向量均衡问题(CVEP)近似拟弱有效解的最优性条件和对偶定理.首先,建立了问题(CVEP)近似拟弱有效解关于近似次微分形式的最优性必要条件.其次,引入了一种广义凸性的概念,称之为近似伪拟type-I函数,并在其假设下,获得了问题(CVEP)近似拟弱有效解的最优性充分条件.最后,引入了问题(CVEP)的广义近似Mond-Weir对偶模型,并建立其与原问题间关于近似拟弱有效解的对偶定理. 相似文献
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Guo-lin Yu 《高校应用数学学报(英文版)》2017,32(2):225-236
There are two approaches of defining the solutions of a set-valued optimization problem:vector criterion and set criterion.This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives.In the case of vector criterion,some optimality conditions are derived for isolated (weak) minimizers.With set criterion,necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation. 相似文献
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Necessary optimality conditions for efficient solutions of unconstrained and vector equilibrium problems with equality and inequality constraints are derived. Under assumptions on generalized convexity, necessary optimality conditions for efficient solutions become sufficient optimality conditions. Note that it is not required here that the ordering cone in the objective space has a nonempty interior. 相似文献
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向量映射的鞍点和Lagrange对偶问题 总被引:4,自引:0,他引:4
本文研究拓扑向量空间广义锥-次类凸映射向量优化问题的鞍点最优性条件和Lagrange对偶问题,建立向量优化问题的Fritz John鞍点和Kuhn-Tucker鞍点的最优性条件及其与向量优化问题的有效解和弱有效解之间的联系。通过对偶问题和向量优化问题的标量化刻画各解之间的关系,给出目标映射是广义锥-次类凸的向量优化问题在其约束映射满足广义Slater约束规格的条件下的对偶定理。 相似文献
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Tran Van Su 《4OR: A Quarterly Journal of Operations Research》2018,16(2):173-198
This article presents necessary and sufficient optimality conditions for weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution of vector equilibrium problem without constraints in terms of contingent derivatives in Banach spaces with stable functions. Using the steadiness and stability on a neighborhood of optimal point, necessary optimality conditions for efficient solutions are derived. Under suitable assumptions on generalized convexity, sufficient optimality conditions are established. Without assumptions on generalized convexity, a necessary and sufficient optimality condition for efficient solutions of unconstrained vector equilibrium problem is also given. Many examples to illustrate for the obtained results in the paper are derived as well. 相似文献
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In this paper, by using the notion of strong subdifferential and epsilon-subdifferential, necessary optimality conditions are established firstly for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a vector optimization problem, where its objective function and constraint set are denoted by using differences of two vector-valued maps, respectively. Then, by using the concept of approximate pseudo-dissipativity, sufficient optimality conditions are obtained. As an application of these results, sufficient and necessary optimality conditions are also given for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a vector fractional mathematical programming. 相似文献
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In this paper, we are concerned with a differentiable multiobjective programming problem in topological vector spaces. An alternative theorem for generalized K subconvexlike mappings is given. This permits the establishment of optimality conditions in this context: several generalized Fritz John conditions, in line to those in Hu and Ling [Y. Hu, C. Ling, The generalized optimality conditions of multiobjective programming problem in topological vector space, J. Math. Anal. Appl. 290 (2004) 363-372] are obtained and, in the presence of the generalized Slater's constraint qualification, the Karush-Kuhn-Tucker necessary optimality conditions. 相似文献
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Nguyen Quang Huy Do Sang Kim Nguyen Van Tuyen 《Journal of Optimization Theory and Applications》2017,174(3):728-745
In the present paper, we establish some results for the existence of optimal solutions in vector optimization in infinite-dimensional spaces, where the optimality notion is understood in the sense of generalized order (may not be convex and/or conical). This notion is induced by the concept of set extremality and covers many of the conventional notions of optimality in vector optimization. Some sufficient optimality conditions for optimal solutions of a class of vector optimization problems, which satisfies the free disposal hypothesis, are also examined. 相似文献
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In this paper we develop the necessary conditions of optimality for a class of distributed parameter systems (partial differential equations) determined by operator valued measures and controlled by vector measures. Based on some recent results on existence of optimal controls from the space of vector measures, we develop necessary conditions of optimality for a class of control problems. The main results are the necessary conditions of optimality for problems without state constraints and those with state constraints. Also, a conceptual algorithm along with a brief discussion of its convergence is presented. 相似文献
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In this paper, we study second-order optimality conditions for multiobjective optimization problems. By means of different
second-order tangent sets, various new second-order necessary optimality conditions are obtained in both scalar and vector
optimization. As special cases, we obtain several results found in the literature (see reference list). We present also second-order
sufficient optimality conditions so that there is only a very small gap with the necessary optimality conditions.
The authors thank Professor P.L. Yu and the referees for valuable comments and helpful suggestions. 相似文献