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Recent Advances and Historical Development of Vector Optimization

Proceedings of an International Conference on Vector Optimization Held at the Technical University of Darmstadt, FRG, August 4–7, 1986

  • Conference proceedings
  • © 1987

Overview

Editors:
  1. Johannes Jahn

    1. Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

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  2. Werner Krabs

    1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Darmstadt, Germany

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 294)

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Table of contents (25 papers)

  1. Front Matter

    Pages N2-VII
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  2. Historical Retrospect

    1. Front Matter

      Pages 1-1
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    2. Initiators of Multicriteria Optimization

      • W. Stadler
      Pages 3-47

  3. Mathematical Theory

    1. Front Matter

      Pages 49-49
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    2. Well Posedness of Vector Optimization Problems

      • Ewa Bednarczuk
      Pages 51-61

    3. Convex Cones, Minimality Notions, and Consequences

      • J. M. Borwein
      Pages 62-85

    4. Evaluation Functionals are the Extreme Points of a Basis for the Dual de C 1 + [a,b]

      • A. R. da Silva
      Pages 86-95

    5. Polarities and Stability in Vector Optimization

      • S. Dolecki, C. Malivert
      Pages 96-113

    6. Sets of Efficiency in a Normed Space and Inner Product

      • Roland Durier
      Pages 114-128

    7. Recent Results on Duality in Vector Optimization

      • K.-H. Elster, A. Göpfert
      Pages 129-136

    8. A Result of Farkas Type and Duality in Vector Optimization

      • Joachim Gwinner
      Pages 137-145

    9. Parametric Optimization with a Bottleneck Objective and Vector Optimization

      • Siegfried Helbig
      Pages 146-159

    10. Duality in Partially Ordered Sets

      • Johannes Jahn
      Pages 160-172

    11. Generating Nested Subsets of Efficient Solutions

      • Ignacy Kaliszewski
      Pages 173-182

    12. Hierarchical Structures in Multicriteria Decision Making

      • Ulrich Krause
      Pages 183-193

    13. Well Posedness, Towards Vector Optimization

      • Roberto Lucchetti
      Pages 194-207

    14. On Some Applications of Stochastic Dominance in Multiobjective Decision-Making

      • Leonid I. Polishchuck
      Pages 208-221

    15. Some Considerations about Computational Complexity for Multi Objective Combinatorial Problems

      • Paolo Serafini
      Pages 222-232

    16. On the Existence of Cone-Efficient Points

      • Alicia Sterna-Karwat
      Pages 233-240

    17. Pseudo-Utilities

      • Andrzej Wieczorek
      Pages 241-253
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Keywords

About this book

In vector optimization one investigates optimization problems in an abstract setting which have a not necessarily real-valued objective function. This scientific discipline is closely related to multi-objective optimization and multi-criteria decision making. This book contains refereed contributions to the "International Conference on Vector Optimization" held at the Technical University of Darmstadt from August 4-7, 1986. This meeting was an interdisciplinary forum devoted to new results in the theory, to applications as well as to the solution of vector optimization problems which are relevant in practice. Because of the great variety of topics covered by the contributions, the 25 articles of this volume are organized in different sections: Historical retrospect, mathematical theory, goal setting and decision making, engineering applications, and related topics. The papers of the invited State-of-the-Art Tutorials given by Professors J.M. Borwein, H. Eschenauer, W. Stadler and P.L. Yu are also included.

Editors and Affiliations

  • Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Johannes Jahn

  • Fachbereich Mathematik, Technische Hochschule Darmstadt, Darmstadt, Germany

    Werner Krabs

Bibliographic Information

  • Book Title: Recent Advances and Historical Development of Vector Optimization

  • Book Subtitle: Proceedings of an International Conference on Vector Optimization Held at the Technical University of Darmstadt, FRG, August 4–7, 1986

  • Editors: Johannes Jahn, Werner Krabs

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-46618-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-18215-3Published: 26 August 1987

  • eBook ISBN: 978-3-642-46618-2Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: VII, 405

  • Topics: Operations Research/Decision Theory

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