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Convex Optimization in Normed Spaces

Theory, Methods and Examples

  • Book
  • © 2015

Overview

Authors:
  1. Juan Peypouquet

    1. Universidad Técnica Federico, Valparaíso, Chile

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  • Self-contained, including all necessary functional and convex analysis background
  • Blends theory and practice, focusing on algorithms, examples and applications
  • Complete yet concise, both in depth and bibliography

Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI, volume 0)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Basic Functional Analysis

    • Juan Peypouquet
    Pages 1-23

  3. Existence of Minimizers

    • Juan Peypouquet
    Pages 25-32

  4. Convex Analysis and Subdifferential Calculus

    • Juan Peypouquet
    Pages 33-64

  5. Examples

    • Juan Peypouquet
    Pages 65-80

  6. Problem-Solving Strategies

    • Juan Peypouquet
    Pages 81-91

  7. Keynote Iterative Methods

    • Juan Peypouquet
    Pages 93-117

  8. Back Matter

    Pages 119-124
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Keywords

About this book

This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.

Reviews

“This short book is dedicated to convex optimization, beginning with theoretical aspects, ending with numerical methods, and complemented with numerous examples. … this is an interesting and well-written book that is adequate for a graduate-level course on convex optimization.” (Constantin Zălinescu, Mathematical Reviews, November, 2015)

Authors and Affiliations

  • Universidad Técnica Federico, Valparaíso, Chile

    Juan Peypouquet

About the author

Juan Peypouquet is an Associate Professor at the Mathematics Department of the Universidad Tecnica Federico Santa Maria.  His main research interest is the study of the asymptotic behavior of dynamical systems in a broad sense, along with their applications in variational analysis and optimization.

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