Maxima and Minima with Applications: Practical Optimization and Duality

ISBN-13: 9780471252894 / Angielski / Twarda / 1998 / 296 str.

Wilfred Kaplan

Opis

Maximum and minimum problems are of daily concern in industry and government operations. These problems are the foundation of optimisation, determining the best manner in which to organise or produce items. By optimising a procedure, costs can be significantly lowered and the waste of materials can be reduced.

Spis treści

Maxima and Minima in Analytic Geometry.

Side Conditions.

Optimization.

Fenchel–Rockafellar Duality Theory.

Appendix.

Answers to Selected Problems.

Index.

O autorze

WILFRED KAPLAN is Professor Emeritus in the Department of Mathematics at the University of Michigan in Ann Arbor. During 45 years of teaching and research, Professor Kaplan has written seven books, including the highly acclaimed Calculus and Linear Algebra, coauthored by Donald Lewis.

Blurb

This new work by Wilfred Kaplan, the distinguished author of influential mathematics and engineering texts, is destined to become a classic. Timely, concise, and content–driven, it provides an intermediate–level treatment of maxima, minima, and optimization. Assuming only a background in calculus and some linear algebra, Professor Kaplan presents topics in order of difficulty. In four short chapters, he describes basic concepts and geometric aspects of maxima and minima, progresses to problems with side conditions, introduces optimization and programming, and concludes with an in–depth discussion of research topics involving the duality theorems of Fenchel and Rockafellar. Throughout the text, the subject of convexity is gradually developed–from its theoretical underpinnings to problems, and finally, to its role in applications. Other features include:
∗ A strong emphasis on practical applications of maxima and minima
∗ An impressive array of supporting topics such as numerical analysis
∗ An ample number of examples and problems
∗ More than 60 illustrations highlighting the text
∗ Algorithms to reinforce concepts
∗ An appendix reviewing the prerequisite linear algebra

Maxima and Minima with Applications is an ideal text for upper–undergraduate and graduate students taking courses in operations research, management, general engineering, and applied mathematics. It can also be used to supplement courses on linear and nonlinear optimization. This volume′s broad scope makes it an excellent reference for professionals wishing to learn more about cutting–edge topics in optimization and mathematical programming.