## Psychology Dictionary of ArgumentsHome | |||

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Linear programming: Linear programming (LP) is a mathematical method for optimizing a linear function, subject to linear constraints. An LP problem typically consists of two parts, an objective function, and a set of constraints. See also Computer programming, Software, Computers._____________ Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||

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Peter Norvig on Linear Programming - Dictionary of Arguments Norvig I 155 Linear Programming/Norvig/Russell: Linear programming (LP) was first studied systematically by the Russian mathematician Leonid Kantorovich (1939) ^{(1)}. It was one of the first applications of computers; the simplex algorithm (Dantzig, 1949)^{(2)} is still used despite worst-case exponential complexity. Karmarkar (1984) ^{(3)} developed the far more efficient family of interior-point methods, which was shown to have polynomial complexity for the more general class of convex optimization problemsby Nesterov and Nemirovski (1994) ^{(4)}. Excellent introductions to convex optimization are provided by Ben-Tal and Nemirovski (2001)^{(5)} and Boyd and Vandenberghe (2004)^{(6)}.1. Kantorovich, L. V. (1939). Mathematical methods of organizing and planning production. Publishd in translation in Management Science, 6(4), 366–422, July 1960. 2. Dantzig, G. B. (1949). Programming of interdependent activities: II. Mathematical model. econometrica, 17, 200–211. 3. Karmarkar, N. (1984). A new polynomial-time algorithm for linear programming. Combinatorica, 4, 373–395. 4. Nesterov, Y. and Nemirovski, A. (1994). Interior-Point Polynomial Methods in Convex Programming. SIAM (Society for Industrial and Applied Mathematics). 5. Ben-Tal, A. and Nemirovski, A. (2001). Lectures on Modern Convex Optimization: Analysis, algorithms, and Engineering Applications. SIAM (Society for Industrial and Applied Mathematics). 6. Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press. _____________ Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |

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