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4 edition of Mathematical vector optimization in partially ordered linear spaces found in the catalog.

Mathematical vector optimization in partially ordered linear spaces

Jahn, Johannes

# Mathematical vector optimization in partially ordered linear spaces

• 245 Want to read
• 6 Currently reading

Published by Lang in Frankfurt am Main, New York .
Written in English

Subjects:
• Mathematical optimization.,
• Vector spaces.,
• Linear topological spaces.

• Edition Notes

Classifications The Physical Object Statement Johannes Jahn. Series Methoden und Verfahren der mathematischen Physik,, Bd. 31 LC Classifications QA402.5 .J34 1986 Pagination 310 p. ; Number of Pages 310 Open Library OL2766364M ISBN 10 3820489401 LC Control Number 86124431 OCLC/WorldCa 13761104

Optimization of ordered sets‎ (4 P) P Stochastic optimization‎ (2 C, 22 P) V Optimization in vector spaces‎ (2 C, 7 P) Pages in category "Mathematical optimization" The following pages are in this category, out of total. This list may not reflect recent changes.   The following lemma is similar to the generalized Hahn-Banach theorem [7, page ] and [4, Lemma 1]. Lemma Let be a real linear space, and let be a real order complete PL space. Let the set be convex. Let be a real linear proper subspace of, with, where for be a concave operator such that whenever there exists a concave operator such that (i) is an extension of Author: Jian-wen Peng, Wei-dong Rong, Jen-Chih Yao. Equivalence of Linear Complementarity Problems and Linear Programs in Vector Lattice Hilbert Spaces the weak minimal element in ordered spaces. Journal of Mathematical Analysis and Applications , M. Seetharama Gowda. () Complementarity Problems over Locally Compact Cones. SIAM Journal on Control and Optimization , Cited by: component functions. Moreover, conjugate duality for cone d.c. optimization is discussed and weak duality theorem is proved in a more general partially ordered linear topological vector space (generalizing the results in [11]). Keywords Multi objective optimization, Cone d.c. programming, Optimality conditions, Conjugate duality.

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### Mathematical vector optimization in partially ordered linear spaces by Jahn, Johannes Download PDF EPUB FB2

In vector optimization one investigates optimal elements such as minimal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The problem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem.

The authors take the reader on a wide-ranging journey from basic mathematical tools of partially ordered spaces to solution algorithms for some of the motivating applications. it balances theory and applications well. The book is written for advanced graduate students or researchers in mathematical optimization."Cited by: Mathematical vector optimization in partially ordered linear spaces book vector optimization in partially ordered linear spaces.

Frankfurt am Main ; New York: Lang, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Johannes Jahn.

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 : Springer-Verlag Berlin Heidelberg.

"The book presents theory and applications of optimization problems in partially ordered spaces with emphasis on the authors’ profound research results. The book should be a must for each scientist dealing with vector optimization theory. It delivers new insights for researchers interested in the solution of vector optimization problems.

1 Linear Spaces Mathematical vector optimization in partially ordered linear spaces book Linear Spaces and Convex Sets 1 Partially Ordered Linear Spaces 9 Topological Linear Spaces 19 Some Examples 30 2 Mappings on Linear Spaces 35 Convex Mappings 35 Differentiable Mappings 41 3 Some Fundamental Theorems 57 Zorn's Lemma and the Hahn-Banach Theorem 57 Separation Theorems 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. About Mathematical vector optimization in partially ordered linear spaces book book Introduction In mathematical modeling of processes one often encounters optimization problems involving more than one objective function, so that Multiobjective Optimization (or Vector Optimization) has received new impetus.

For professionals and graduate students in engineering, mathematics, operations research, economics, and business and finance, Optimization Mathematical vector optimization in partially ordered linear spaces book Vector Space Methods is an indispensable source of problem-solving by: In vector optimization one investigate optimal elements of a nonempty set E of a partially ordered linear space Y.

Problems of this type can be found not only in mathematics but also in other elds such as engineering or economics. For instance, due to the natural order of a cone, it plays a vital role in the study of partially ordered spaces and vector optimization (see, [1, 6]).

Similarly, in mathematical economics (see. Johannes Jahn, Mathematical vector optimization in partially ordered linear spaces, Methoden und Verfahren der Mathematischen Physik [Methods and Procedures in Mathematical Physics], vol.

31, Verlag Peter D. Lang, Frankfurt am Main, MR ; Johannes Jahn, Scalarization in vector optimization, Math. From a mathematical point of view, a vector optimization problem consists of the research of those values which will be defined as optimal in the partidlly ordered set Z = f{S) C FIP.

The set Z is called the image space under the mapping / or the outcome space. Existence of Solutions for Vector Optimization Problems and prove the existence of the generalized efficient solution for nondifferentiable vector optimization problems by using vector variational-like inequalities for set-valued maps.

Mathematical Vector Optimization Mathematical vector optimization in partially ordered linear spaces book Partially Ordered Linear Spaces, Verlag Peter Lang ()Cited by: tions to vector optimization problems with a variable ordering structure. In vector optimization with a partially ordered linear space, the notion of proper optimal ele-ments is very important from a theoretical and practical points of view.

For instance, using linear scalarization, properly optimal elements can be completely character. The presentation is given in a very general setting, working in general linear and linear topological spaces sometimes specialized to normed spaces.

Of course, as it is natural for vector optimization, partially ordered (by convex cones) linear spaces and their most important features (convex cones, dual cones, order intervals etc.) are introduced.

Mathematical Vector Optimization in Partially-Ordered Linear Spaces, Verlag Peter Lang, (). Multiobjective Decision Making: Theory and Methodology. mapping in an arbitrary real linear space Y. The space Y may be partially ordered (for the deﬁnition of a partial ordering see Deﬁnition ).

Using this partial order-ing, several optimality notions can be deﬁned. In Section 3 we give an introduction to vector optimization in partially ordered spaces. The discussed concepts and a. Variational Sets of Perturbation Maps and Applications to Sensitivity Analysis for Constrained Vector Optimization.

Journal of Optimization Theory and Applications, Vol.Issue. 2, p. Mathematical vector optimization in partially ordered linear spaces (Peter Lang First-order optimality conditions in set-valued optimization Cited by: J.

Jahn, "Mathematical Vector Optimization in Partially Order Linear Spaces,", Methoden und Verfahren der Mathematischen Physik [Methods and Procedures in Mathematical Physics], 31 (). Google Scholar [14] S. Kutateladze, Convex $\varepsilon$-programming, Soviet Math. Dokl., 20 (), Google Scholar [15]Cited by: 5.

Vector optimization is a subarea of mathematical optimization where optimization problems with a vector-valued objective functions are optimized with respect to a given partial ordering and subject to certain constraints. A multi-objective optimization problem is a special case of a vector optimization problem: The objective space is the finite dimensional Euclidean space partially ordered by the component-wise.

financial optimization. The book uses functional analysis—the study of linear vector spaces—to impose simple, intuitive interpretations on complex, infinite-dimensional problems. The early chapters offer an introduction to functional analysis, with applications to optimization.

Topics addressed include linear space,File Size: 6MB. Book Review Book Review DOI /s Go¨ pfert, Alfred; Riahi, Hassan; Tammer, Christiane and Za˘ linescu, Constantin: Variational Methods in Partially Ordered Spaces.

Springer-Verlag, New York, Berlin, HeidelbergISBN The book presents theory and applications of optimization problems in partially ordered spaces with. space as introduced in [62] is precisely the part of the structure of a linear space which remains invariant under passing to the power set (with Minkowski addition) or order completion (add a least and greatest element to an ordered vector space).

Thus, IR ∪ {−∞,+∞} is the prototype of a conlinear space. A particular feature is the File Size: KB. where is a parameter vector. Let be the set of all Pareto optimal values in the objective space to ().The set-valued mapping is considered to be a generalization of the marginal (optimal-value) function in ordinary scalar optimization.

The behaviour of has been analyzed both qualitatively and quantitatively. Several types of duality, such as Lagrange duality, Wolfe duality, and conjugate. function of the primal problem is partially ordered by the corresponding non-negative orthant, we introduced in [1] a new vector dual to the classical linear vector optimization problem, for the situation when an arbitrary pointed convex cone partially ordered the mentioned image space, overcoming the drawbacks of the mentioned duals.

Mathematical vector optimization in partially ordered linear spaces. Peter Lang, (). Molho: Scalarization and its stability in vector optimization.

In vector optimization the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative orthant. We consider extensions of the projected gradient gradient method to vector optimization, which work directly with vector-valued functions, without using Cited by:   This paper deals with the stability of systems of linear inequalities in partially ordered Banach spaces when the data are subjected to small perturbations.

We show that a certain condition is necessary and sufficient for such by: E. Hern´andez, B. Jim´enez, V. Novo / Proper Eﬃciency in Set-Valued Optimization 2. Notations and preliminaries Throughout this paper we consider a real linear space Y partially ordered by a convex cone Kin Y.

Let A⊂ Y, we denote by cone(A), conv(A), aﬀ(A), span(A) and L(A). Mathematical Methods of Physics/Vector Spaces. From Wikibooks, open books for an open world to facilitate its further use in Physics. The interested reader is encouraged to look up the Wikibook Linear Algebra for details regarding the intricacies of the topic.

Contents. 1 Book:Mathematical Methods of Physics; Navigation menu. Personal. On linear vector optimization duality in infinite-dimensional spaces Article (PDF Available) in Numerical Algebra 1(3) September with 27 Reads How we measure 'reads'.

The vector optimization problems we consider in this note consist of vector-minimizing or vector-maximizing a vector function with respect to the partial order-ing induced in the image space of the vector function by a nontrivial pointed closed convex cone.

For the vector-minimization problems we use the notation Min, while. American Mathematical Society Charles Street Providence, Rhode Island or AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American Mathematical Society and registered in the U.S.

Patent and Trademark. WEAK E-OPTIMAL SOLUTION IN VECTOR OPTIMIZATION Zhao, Ke-Quan, Yang, Xin-Min, and Peng, Jian-Wen, Taiwanese Journal of Mathematics, ; Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps Hu, Xiaohong, Fang, Zhimiao, and Xiong, Yunxuan, Abstract and Applied Analysis, Cited by: 5.

Get this from a library. Variational methods in partially ordered spaces. [A Göpfert;] -- In mathematical modeling of processes one often encounters optimization problems involving more than one objective function, so that Multiobjective Optimization (or Vector Optimization) has received.

This paper considers the parametric primal and dual vector equilibrium problems in locally convex Hausdorff topological vector spaces. Based on linear scalarization technique, we establish sufficient conditions for the continuity of approximate solution maps to these problems.

As applications, some new results for vector optimization problem and vector variational inequality are : Lam Quoc Anh, Pham Thanh Duoc, Tran Ngoc Tam.

The concept of nonlinear split ordered variational inequality problems on partially ordered Banach spaces extends the concept of the linear split vector variational inequality problems on Banach spaces, while the latter is a natural extension of vector variational inequality problems on Banach : Jinlu Li.

In this paper, by using the generalization of Ljusternik theorem, the open mapping theorem of convex process, and the convex sets separation theorem, we give the necessary conditions for the efficient solution to the constrained vector equilibrium problems without requiring that the ordering cone in the objective space has a nonempty interior and without requiring that the the convexity Cited by: 7.

Vector optimization problems are a significant extension of multiobjective optimization, which has a large number of real life applications.

In vector optimization the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative orthant. ods in Partially Ordered Spaces, volume 17 of CMS Books in Pdf.

Springer-Verlag, New York, [45] GOPFERT, A., TAMMER, C. and Z¨ ALINESCU, C. On the vectorial Ekeland’s˘ variational principle and minimal points in product spaces.

Report of the Institut of Optimization and Stochast Martin-Luther-University Halle-Wittenberg.In this paper, the notion of ∊-strictly efficient solution for vector optimization with set-valued maps is introduced. Under the assumption of the ic-cone-convexlikeness for set-valued maps, the sc Cited by: 9.We investigate the connections ebook vector variational inequalities and ordered variational inequalities in finite dimensional real vector spaces.

We also use some fixed point theorems to prove the solvability of ordered variational inequality problems and their application to some order-optimization problems on the Banach by: 1.