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＜電子ブック＞
Linear Optimization and Approximation : An Introduction to the Theoretical Analysis and Numerical Treatment of Semi-infinite Programs / by K. Glashoff, S.-A. Gustafson
(Applied Mathematical Sciences. ISSN:2196968X ; 45)

版	1st ed. 1983.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1983
本文言語	英語
大きさ	212 p : online resource
冊子体	Linear optimization and approximation : an introduction to the theoretical analysis and numerical treatment of semi-infinite programs / Klaus Glashoff, Sven-Åke Gustafson ; : U.S,: Germany
著者標目	*Glashoff, K author Gustafson, S.-A author SpringerLink (Online service)
件　名	LCSH:System theory LCSH:Control theory LCSH:Mathematical optimization LCSH:Calculus of variations FREE:Systems Theory, Control FREE:Calculus of Variations and Optimization
一般注記	I. Introduction and Preliminaries -- II. Weak Duality -- III. Applications of Weak Duality in Uniform Approximation -- IV. Duality Theory -- V. The Simplex Algorithm -- VI. Numerical Realization of The Simplex Algorithm -- VII. A General Three-Phase Algorithm -- VIII. Approximation Problems by Chebyshev Systems -- IX. Examples and Applications of Semi-Infinite Programming -- References 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-1142-6

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