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Foundations of Optimization

  • Book
  • © 1976

Overview

Authors:
  1. M. S. Bazaraa

    1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA

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    You can also search for this author in PubMed   Google Scholar

  2. C. M. Shetty

    1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 122)

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Table of contents (9 chapters)

  1. Front Matter

    Pages N2-VI
    Download chapter PDF

  2. Convex Analysis

    1. Linear Subspaces and Affine Manifolds

      • M. S. Bazaraa, C. M. Shetty
      Pages 1-14

    2. Convex Sets

      • M. S. Bazaraa, C. M. Shetty
      Pages 15-53

    3. Convex Cones

      • M. S. Bazaraa, C. M. Shetty
      Pages 54-87

    4. Convex Functions

      • M. S. Bazaraa, C. M. Shetty
      Pages 88-113

  3. Optimality Conditions and Duality

    1. Stationary Point Optimality Conditions with Differentiability

      • M. S. Bazaraa, C. M. Shetty
      Pages 114-132

    2. Constraint Qualifications

      • M. S. Bazaraa, C. M. Shetty
      Pages 133-154

    3. Convex Programming without Differentiability

      • M. S. Bazaraa, C. M. Shetty
      Pages 155-168

    4. Lagrangian Duality

      • M. S. Bazaraa, C. M. Shetty
      Pages 169-176

    5. Conjugate Duality

      • M. S. Bazaraa, C. M. Shetty
      Pages 177-191

  4. Back Matter

    Pages 192-198
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Keywords

About this book

Current1y there is a vast amount of literature on nonlinear programming in finite dimensions. The pub1ications deal with convex analysis and severa1 aspects of optimization. On the conditions of optima1ity they deal mainly with generali- tions of known results to more general problems and also with less restrictive assumptions. There are also more general results dealing with duality. There are yet other important publications dealing with algorithmic deve10pment and their applications. This book is intended for researchers in nonlinear programming, and deals mainly with convex analysis, optimality conditions and duality in nonlinear programming. It consolidates the classic results in this area and some of the recent results. The book has been divided into two parts. The first part gives a very comp- hensive background material. Assuming a background of matrix algebra and a senior level course in Analysis, the first part on convex analysis is self-contained, and develops some important results needed for subsequent chapters. The second part deals with optimality conditions and duality. The results are developed using extensively the properties of cones discussed in the first part. This has faci- tated derivations of optimality conditions for equality and inequality constrained problems. Further, minimum-principle type conditions are derived under less restrictive assumptions. We also discuss constraint qualifications and treat some of the more general duality theory in nonlinear programming.

Authors and Affiliations

  • School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA

    M. S. Bazaraa, C. M. Shetty

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