# Linear Optimization and Approximation

## An Introduction to the Theoretical Analysis and Numerical Treatment of Semi-infinite Programs

Part of the Applied Mathematical Sciences book series (AMS, volume 45)

Advertisement

Part of the Applied Mathematical Sciences book series (AMS, volume 45)

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con straints; in general there may be infinitely many constraints. This book is devoted to such problems. Their mathematical properties are investi gated and algorithms for their computational solution are presented. Applications are discussed in detail. Linear optimization problems are encountered in many areas of appli cations. They have therefore been subject to mathematical analysis for a long time. We mention here only two classical topics from this area: the so-called uniform approximation of functions which was used as a mathematical tool by Chebyshev in 1853 when he set out to design a crane, and the theory of systems of linear inequalities which has already been studied by Fourier in 1823. We will not treat the historical development of the theory of linear optimization in detail. However, we point out that the decisive break through occurred in the middle of this century. It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

Approximation Dualität (Math.) Lineare Optimierung algorithms calculus linear optimization optimization

- DOI https://doi.org/10.1007/978-1-4612-1142-6
- Copyright Information Springer-Verlag New York Inc. 1983
- Publisher Name Springer, New York, NY
- eBook Packages Springer Book Archive
- Print ISBN 978-0-387-90857-1
- Online ISBN 978-1-4612-1142-6
- Series Print ISSN 0066-5452
- Buy this book on publisher's site