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Titlebook: Vector Optimization; Theory, Applications Johannes Jahn Book 20041st edition Springer-Verlag Berlin Heidelberg 2004 Convex Analysis.Derivat

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樓主
發(fā)表于 2025-3-21 18:37:16 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Vector Optimization
副標(biāo)題Theory, Applications
編輯Johannes Jahn
視頻videohttp://file.papertrans.cn/981/980842/980842.mp4
概述Very comprehensive, modern and application-oriented presentation of a general theory of vector optimization: The reader learns all important aspects of vector optimization and how to apply it to concr
圖書封面Titlebook: Vector Optimization; Theory, Applications Johannes Jahn Book 20041st edition Springer-Verlag Berlin Heidelberg 2004 Convex Analysis.Derivat
描述In vector optimization one investigates optimal elements such as min- imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob- lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer- ing and economics. Vector optimization problems arise, for exam- ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland‘s variational principle), multiobjective pro- gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza- tion, seems to have important applications to variational inequalities and optimization problems with m
出版日期Book 20041st edition
關(guān)鍵詞Convex Analysis; Derivative; Multiobjective Optimisation; Multiobjective Optimization; Optimality Condit
版次1
doihttps://doi.org/10.1007/978-3-540-24828-6
isbn_ebook978-3-540-24828-6
copyrightSpringer-Verlag Berlin Heidelberg 2004
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沙發(fā)
發(fā)表于 2025-3-21 23:03:54 | 只看該作者
Some Fundamental Theoremsst, we formulate Zorn’s lemma and the Hahn-Banach theorem and, as a consequence, we examine several types of separation theorems. Moreover, we discuss a James theorem on the characterization of weakly compact sets and we study two Krein-Rutman theorems on the extension of positive linear functionals
板凳
發(fā)表于 2025-3-22 03:47:58 | 只看該作者
Optimality Notionsements of this set. But in certain situations it also makes sense to study several variants of these concepts; for example, strongly minimal, properly minimal and weakly minimal elements (or strongly maximal, properly maximal and weakly maximal elements). It is the aim of this first chapter of the s
地板
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5#
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Generalized Lagrange Multiplier Ruleis rule for the optimization of a real-valued function under side-conditions in the form of equalities. In this context we investigate an abstract optimization problem (introduced in Example 4.5) with equality and inequality constraints. For this problem we derive a generalized multiplier rule as a
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Vector Approximation results known from approximation theory can be extended to this vector-valued case. After a short introduction we examine the relationship between vector approximation and simultaneous approximation, and we present the so-called generalized Kolmogorov condition. Moreover, we consider nonlinear and
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發(fā)表于 2025-3-22 22:19:50 | 只看該作者
Cooperative , Player Differential Gamesers behaving exclusively cooperatively. Such games can be described as vector optimization problems. After some basic remarks on the cooperation concept we present necessary and sufficient conditions for optimal and weakly optimal controls concerning a system of ordinary differential equations. In t
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