Linear Optimization

Ulrich Kulisch, Rolf Hammer, Matthias Hocks and Dietmar Ratz
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Ulrich Kulisch: Universität Karlsruhe, Institut für Angewandte Mathematik
Rolf Hammer: Universität Karlsruhe, Institut für Angewandte Mathematik
Matthias Hocks: Universität Karlsruhe, Institut für Angewandte Mathematik
Dietmar Ratz: Universität Karlsruhe, Institut für Angewandte Mathematik

Chapter Chapter 11 in C++ Toolbox for Verified Computing I, 1995, pp 210-243 from Springer

Abstract: Abstract A linear programming problem consists of a linear function to be maximized (or minimized) subject to linear equality and inequality constraints. Any linear program (LP) can be put by well-known transformations into standard form (11.1) $$\begin{array}{l} (LP)\begin{array}{*{20}{c}} z&{{c^T}x}&{ = \max }\\ {}&{{A_x}}&{ = b}\\ {}&x&{ \ge 0} \end{array}\\ \mathop \Leftrightarrow \limits_{\max \{ {c^T}x|x \in X\} ,X: = \{ x \in {R^n}|Ax = b,x \ge 0\} ,} \end{array}$$ where A is a real m x n matrix, $$ b \in {\mathbb{R}^m},\,c\, \in \,{\mathbb{R}^n}$$ . The input data of (11.1) are given by the triple $$P = (A,b,c)\, \in \,{\mathbb{R}^{m \cdot n + m + n}}$$ .

Keywords: Linear Programming Problem; Linear Optimization; Basic Index; Error Code; Linear Optimization Problem (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-3-642-79651-7_11

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