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Nondifferentiable and Two-Level Mathematical Programming

  • Kiyotaka Shimizu
  • Yo Ishizuka
  • Jonathan F. Bard

Table of contents

  1. Front Matter
    Pages i-xii
  2. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 1-12
  3. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 13-58
  4. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 59-112
  5. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 113-127
  6. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 128-187
  7. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 188-228
  8. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 229-258
  9. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 259-270
  10. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 271-279
  11. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 280-291
  12. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 292-311
  13. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 312-317
  14. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 318-333
  15. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 334-346
  16. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 347-390
  17. Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
    Pages 391-449
  18. Back Matter
    Pages 450-470

About this book

Introduction

The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.

Keywords

algorithm algorithms complex system complex systems linear optimization mathematical programming nonlinear optimization operations research optimization programming system

Authors and affiliations

  • Kiyotaka Shimizu
    • 1
  • Yo Ishizuka
    • 2
  • Jonathan F. Bard
    • 3
  1. 1.Keio UniversityYokohamaJapan
  2. 2.Sophia UniversityTokyoJapan
  3. 3.The University of TexasAustinUSA

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