Overview
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.
Similar content being viewed by others
Keywords
Table of contents (16 chapters)
-
Front Matter
-
Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Nondifferentiable and Two-Level Mathematical Programming
Authors: Kiyotaka Shimizu, Yo Ishizuka, Jonathan F. Bard
DOI: https://doi.org/10.1007/978-1-4615-6305-1
Publisher: Springer New York, NY
-
eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1997
Hardcover ISBN: 978-0-7923-9821-9Published: 30 November 1996
Softcover ISBN: 978-1-4613-7895-2Published: 02 November 2012
eBook ISBN: 978-1-4615-6305-1Published: 06 December 2012
Edition Number: 1
Number of Pages: XII, 470
Topics: Operations Research/Decision Theory, Systems Theory, Control, Mathematical Modeling and Industrial Mathematics