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半无穷向量最优化问题的最优性条件李泽民(重庆建筑大学,630045)1990年8月27日收到.1993年3月1日收到修改、压缩稿.无穷维空间中的向量极值问题已引起了不少学者的兴趣[2-4].本文研究半无穷向量极值问题的最优性条件,得出了一系列有意义的... 相似文献
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本文利用序线性空间中关于次似凸集值映射的择一性定理,得出了具有广义等式和不等式约束的向量极值问题的最优性条件. 相似文献
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本文给出了混合整数二次规划问题的全局最优性条件,包括全局最优充分性条件和全局最优必要性条件.我们还给出了一个数值实例用以说明如何利用本文所给出的全局最优性条件来判定一个给定点是否是全局最优解. 相似文献
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龙宪军 《数学物理学报(A辑)》2014,34(3):593-602
在Asplund空间中,研究了非凸向量均衡问题近似解的最优性条件.借助Mordukhovich次可微概念,在没有任何凸性条件下获得了向量均衡问题εe-拟弱有效解,εe-拟Henig有效解,εe-拟全局有效解以及εe-拟有效解的必要最优性条件.作为它的应用,还给出了非凸向量优化问题近似解的最优性条件. 相似文献
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焦合华 《数学的实践与认识》2010,40(16)
函数的广义凸性在数学规划及数学规划的对偶理论中起着非常重要的作用.在一种函数的广义凸性-关于n和b的B-(p,γ)-不变凸性的假设下,讨论了一类含有无穷多分式函数的约束广义分式规划及其对偶的某些问题:首先,给出并证明了这类约束广义分式规划的一个最优性充分条件,接着,针对这一类广义分式规划,提出了它的一个混合型对偶,然后又在适当的条件下,进一步给出并证明了相应的弱对偶定理,强对偶定理以及严格逆对偶定理. 相似文献
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本文在序线性空间中建立了广义次似凸映射下的择一定理,运用此定理,得出一类向量极值问题的最优性条件. 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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M. Durea 《Journal of Global Optimization》2010,47(1):13-27
The aim of this paper is to study optimality conditions for strict local minima to constrained mathematical problems governed
by scalar and vectorial mappings. Unlike other papers in literature dealing with strict efficiency, we work here with mappings
defined on infinite dimensional normed vector spaces. Firstly, we (mainly) consider the case of nonsmooth scalar mappings
and we use the Fréchet and Mordukhovich subdifferentials in order to provide optimality conditions. Secondly, we present some
methods to reduce the study of strict vectorial minima to the case of strict scalar minima by means of some scalarization
techniques. In this vectorial framework we treat separately the case where the ordering cone has non-empty interior and the
case where it has empty interior. 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 propose weak separation functions in the image space for general constrained vector optimization problems on strong and weak vector minimum points. Gerstewitz function is applied to construct a special class of nonlinear separation functions as well as the corresponding generalized Lagrangian functions. By virtue of such nonlinear separation functions, we derive Lagrangian-type sufficient optimality conditions in a general context. Especially for nonconvex problems, we establish Lagrangian-type necessary optimality conditions under suitable restriction conditions, and we further deduce Karush–Kuhn–Tucker necessary conditions in terms of Clarke subdifferentials. 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 these comments on the excellent survey by Dinh and Jeyakumar, we briefly discuss some recently developed topics and results on applications of extended Farkas’ lemma(s) and related qualification conditions to problems of variational analysis and optimization, which are not fully reflected in the survey. They mainly concern: Lipschitzian stability of feasible solution maps for parameterized semi-infinite and infinite programs with linear and convex inequality constraints indexed by arbitrary sets; optimality conditions for nonsmooth problems involving such constraints; evaluating various subdifferentials of optimal value functions in DC and bilevel infinite programs with applications to Lipschitz continuity of value functions and optimality conditions; calculating and estimating normal cones to feasible solution sets for nonlinear smooth as well as nonsmooth semi-infinite, infinite, and conic programs with deriving necessary optimality conditions for them; calculating coderivatives of normal cone mappings for convex polyhedra in finite and infinite dimensions with applications to robust stability of parameterized variational inequalities. We also give some historical comments on the original Farkas’ papers. 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
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In this paper, we establish sufficient optimality conditions for D.C. vector optimization problems. We also give an application to vector fractional mathematical programming in a ordred separable Hilbert space. 相似文献
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The purpose of this paper is to establish optimality conditions for vector equilibrium problems with constraints. By using
the separation of convex sets, we obtain the necessary and sufficient conditions for the Henig efficient solution and the
superefficient solution to the vector equilibrium problem with constraints. As applications of our results, we derive some
optimality conditions to the vector variational inequality problem and the vector optimization problem with constraints. 相似文献
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The aim of this paper is to provide global optimality conditions and duality results for a class of nonconvex vector optimization problems posed on Banach spaces. In this paper, we introduce the concept of quasi type I α-invex, pseudo type I α-invex, quasi pseudo type I α-invex, and pseudo quasi type I α-invex functions in the setting of Banach spaces, and we consider a vector optimization problem with functions defined on Banach spaces. A few sufficient optimality conditions are given, and some results on duality are proved. 相似文献
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This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints,denoted by(MMOP).More precisely,we first establish necessary conditions for optimal solutions to the problem(MMOP)by means of employing some advanced tools of variational analysis and generalized differentiation.Then,sufficient conditions for the existence of such solutions to the problem(MMOP)are investigated with the help of generalized convexity functions defined in terms of the limiting subdifferential of locally Lipschitz functions.Finally,some of the obtained results are applied to formulating optimality conditions for weakly efficient solutions to a related multiobjective optimization problem with an infinite number of constraints,and a necessary optimality condition for a quasiε-solution to problem(MMOP). 相似文献