Nonlinear Programming - Hardcover

Hardcover

ISBN 10: 0882759191 ISBN 13: 9780882759197

Publisher: Krieger Pub Co, 1979

Synopsis

This reprint of the 1969 book of the same name is a concise, rigorous,
yet accessible account of the fundamentals of constrained optimization
theory. Many problems arising in diverse fields such as machine
learning, medicine, chemical engineering, structural design, and
airline scheduling can be reduced to a constrained optimization
problem. This book provides readers with the fundamentals needed to
study and solve such problems.

Beginning with a chapter on linear inequalities and theorems of the
alternative, basics of convex sets and separation theorems are then
derived based on these theorems. This is followed by a chapter on
convex functions that includes theorems of the alternative for such
functions. These results are used in obtaining the saddlepoint
optimality conditions of nonlinear programming without
differentiability assumptions. Properties of differentiable convex
functions are derived and then used in two key chapters of the book,
one on optimality conditions for differentiable nonlinear programs and
one on duality in nonlinear programming. Generalizations of convex
functions to pseudoconvex and quasiconvex functions are given and then
used to obtain generalized optimality conditions and duality results
in the presence of nonlinear equality constraints.

The book has four useful self-contained appendices on vectors and
matrices, topological properties of n-dimensional real space,
continuity and minimization, and differentiable functions.

Audience

Undergraduates with an advanced calculus background and graduate
students in computer science, industrial engineering, operations
research, electrical engineering, economics, business, mathematics,
and civil and mechanical engineering will find this book of great use.
It will also be of interest to researchers in oil, investment,
chemical, and software companies, as well as banks and airlines.

About the Author

Olvi L. Mangasarian is the John von Neumann Professor of Mathematics
and Computer Sciences at the University of Wisconsin, Madison.

About this title

Book Description

A concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and scheduling can be reduced to a constrained optimization problem. Provides readers with the fundamentals needed to study and solve such problems.

Edition details

• Publisher: Krieger Pub Co
• Publication date: 1979
• ISBN 10: 0882759191
• ISBN 13: 9780882759197
• Binding: Hardcover
• Language: English
• Number of pages: 220
• Editor: Mangasarian Olvi L.