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Separable Programming

Theory and Methods

  • Book
  • © 2001

Overview

Authors:
  1. Stefan M. Stefanov

    1. Department of Mathematics, South West University, Blagoevgrad, Bulgaria

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Part of the book series: Applied Optimization (APOP, volume 53)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xix
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  2. Preliminaries: Convex Analysis and Convex Programming

    1. Preliminaries: Convex Analysis and Convex Programming

      • Stefan M. Stefanov
      Pages 1-61

  3. Separable Programming

    1. Front Matter

      Pages 63-63
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    2. Introduction. Approximating the Separable Problem

      • Stefan M. Stefanov
      Pages 65-77

    3. Convex Separable Programming

      • Stefan M. Stefanov
      Pages 79-90

    4. Separable Programming: A Dynamic Programming Approach

      • Stefan M. Stefanov
      Pages 91-139

  4. Convex Separable Programming with Bounds on the Variables

    1. Front Matter

      Pages 141-141
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    2. Statement of the Main Problem. Basic Result

      • Stefan M. Stefanov
      Pages 143-150

    3. Version One: Linear Equality Constraints

      • Stefan M. Stefanov
      Pages 151-158

    4. The Algorithms

      • Stefan M. Stefanov
      Pages 159-174

    5. Version Two: Linear Constraint of the Form “≥”

      • Stefan M. Stefanov
      Pages 175-180

    6. Well-Posedness of Optimization Problems. On the Stability of the Set of Saddle Points of the Lagrangian

      • Stefan M. Stefanov
      Pages 181-194

    7. Extensions

      • Stefan M. Stefanov
      Pages 195-206

    8. Applications and Computational Experiments

      • Stefan M. Stefanov
      Pages 207-222

  6. Back Matter

    Pages 269-316
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Keywords

About this book

In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered.
Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed.
As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well.
Audience: Advanced undergraduate and graduate students, mathematical programming/ operations research specialists.

Authors and Affiliations

  • Department of Mathematics, South West University, Blagoevgrad, Bulgaria

    Stefan M. Stefanov

Bibliographic Information

  • Book Title: Separable Programming

  • Book Subtitle: Theory and Methods

  • Authors: Stefan M. Stefanov

  • Series Title: Applied Optimization

  • DOI: https://doi.org/10.1007/978-1-4757-3417-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2001

  • Hardcover ISBN: 978-0-7923-6882-3Published: 31 May 2001

  • eBook ISBN: 978-1-4757-3417-1Published: 11 November 2013

  • Series ISSN: 1384-6485

  • Edition Number: 1

  • Number of Pages: XIX, 314

  • Topics: Optimization

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