共查询到20条相似文献,搜索用时 15 毫秒
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Johannes Jahn Truong Xuan Duc Ha 《Journal of Optimization Theory and Applications》2011,148(2):209-236
In this paper we study a set optimization problem (SOP), i.e. we minimize a set-valued objective map F, which takes values on a real linear space Y equipped with a pre-order induced by a convex cone K. We introduce new order relations on the power set P(Y)\mathcal{P}(Y) of Y (or on a subset of it), which are more suitable from a practical point of view than the often used minimizers in set optimization.
Next, we propose a simple two-steps unifying approach to studying (SOP) w.r.t. various order relations. Firstly, we extend in a unified scheme some basic concepts of vector optimization, which
are defined on the space Y up to an arbitrary nonempty pre-ordered set
(Q,\preccurlyeq)(\mathcal{Q},\preccurlyeq) without any topological or linear structure. Namely, we define the following concepts w.r.t. the pre-order
\preccurlyeq\preccurlyeq: minimal elements, semicompactness, completeness, domination property of a subset of Q\mathcal{Q}, and semicontinuity of a set-valued map with values in Q\mathcal{Q} in a topological setting. Secondly, we establish existence results for optimal solutions of (SOP), when F takes values on
(Q,\preccurlyeq)(\mathcal{Q},\preccurlyeq) from which one can easily derive similar results for the case, when F takes values on P(Y)\mathcal{P}(Y) equipped with various order relations. 相似文献
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§ 9 集 合 组 装 问 题 以下,我们讨论如§5中所给出的准序。对于一个集 合XB_1~n,如果x=(x_1,x_2,…x_n)∈X,存在N={1,2,…,n}上的一个置换π使得 有x_(π(1))x_(π(2))…x_(π(n)),即 对于X是一个线性序,则称X是正则的。 相仿地,对于一个布尔或拟布尔函数f,也可建立准序: 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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Ahmed Sebbar 《Milan Journal of Mathematics》2016,84(2):317-347
We give different linear and nonlinear differential relations on Jacobi theta functions with more emphasis on the nonlinear differential equation of the third order of Jacobi. We present different points of view with a special attention to the role played by the second order linear differential equations, and their link to the Riccati equation and the Schwarzian equation. We also study an identity for theta functions resulting from the action of certain infinite order differential operators. 相似文献
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Mario Petrich 《Semigroup Forum》2006,72(1):36-50
Weakly strict regular semigroups WS represent a generalization
of strict regular semigroups. For the intersection of WS with some
usual e-varieties of regular semigroups, such as left regular
orthodox semigroups and similar e-varieties V, we provide WS
⋂ V with a basis of identities and forbidden semigroups. The
latter, by exclusion, characterize the given e-variety. We do this
also for WS. Coupled with some results of Hall, Churchill and
Trotter, we characterize in this way also the e-varieties of
completely regular semigroups as well as regular semigroups which
are locally completely regular. The e-varieties studied are depicted
in a diagram. 相似文献
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Tomas Ya. Azizov Valerii A. Senderov Viktor A. Khatskevich 《Journal of Mathematical Sciences》2014,200(3):295-304
We consider the theory of operators in spaces with indefinite metric. Strict plus-operators acting between two Krein spaces are considered. A construction showing that, under certain conditions, a strict plus-operator can be considered as a bistrict plus-operator without loss of generality is given. 相似文献
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Ferit Toska 《Archive for Mathematical Logic》2014,53(5-6):525-538
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Singh Sukhjit Gupta D. K. Martínez E. Hueso José L. 《Mediterranean Journal of Mathematics》2016,13(6):4219-4235
Mediterranean Journal of Mathematics - Semilocal convergence for an iteration of order five for solving nonlinear equations in Banach spaces is established under second-order Fréchet... 相似文献
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《Discrete Applied Mathematics》1988,21(2):113-131
A graph G is called a strict 2-threshold graph if its edge-set can be partitioned into two threshold graphs T1 and T2 such that every triangle of G is also a triangle of T1 or of T2. We indicate a polynomial-time algorithm to recognize these graphs and characterize them by forbidden configurations. 相似文献
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Yongdo Lim 《Mathematische Zeitschrift》2000,234(2):407-411