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Foundations of Mathematical Optimization

Convex Analysis without Linearity

  • Book
  • © 1997

Overview

Authors:
  1. Diethard Pallaschke

    1. Institute for Statistics and Mathematical Economics, University of Karlsruhe, Karlsruhe, Germany

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  2. Stefan Rolewicz

    1. Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 388)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. General Optimality

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 1-55

  3. Optimization in Metric Spaces

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 56-170

  4. Multifunctions and marginal functions in metric spaces

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 171-230

  5. Well-posedness and weak well-posedness in Banach spaces

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 231-293

  6. Duality in Banach and Hilbert spaces. Regularization

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 294-312

  7. Necessary conditions for optimality and local optimality in normed spaces

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 313-389

  8. Polynomials. Necessary and sufficient conditions of optimality of higher order

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 390-411

  9. Nondifferentiable optimization

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 412-468

  10. Numerical aspects

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 469-496

  11. Vector optimization

    • Diethard Pallaschke, Stefan Rolewicz
    Pages 497-550

  12. Back Matter

    Pages 551-585
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Keywords

About this book

Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization.
Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.

Authors and Affiliations

  • Institute for Statistics and Mathematical Economics, University of Karlsruhe, Karlsruhe, Germany

    Diethard Pallaschke

  • Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland

    Stefan Rolewicz

Bibliographic Information

  • Book Title: Foundations of Mathematical Optimization

  • Book Subtitle: Convex Analysis without Linearity

  • Authors: Diethard Pallaschke, Stefan Rolewicz

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-017-1588-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1997

  • Hardcover ISBN: 978-0-7923-4424-7Published: 28 February 1997

  • Softcover ISBN: 978-90-481-4800-4Published: 07 December 2010

  • eBook ISBN: 978-94-017-1588-1Published: 14 March 2013

  • Edition Number: 1

  • Number of Pages: XII, 585

  • Topics: Optimization

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