Generalized Goal Programming: polynomial methods and applications |
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Authors: | Emilio Carrizosa Jörg Fliege |
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Institution: | Facultad de Matemáticas, Universidad de Sevilla, Tarfia s/n, 41012 Seville, Spain. e-mail: ecarrizosa@us.es, ES Fachbereich Mathematik, Universit?t Dortmund, 44221 Dortmund, Germany. e-mail: fliege@math.uni-dortmund.de, DE
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Abstract: | In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary
componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming
problems, as well as several models in Location and Regression Analysis are modeled within this framework.
In spite of its generality, this problem can be analyzed from a geometrical and a computational viewpoint, and a unified solution
methodology can be given. Indeed, a dual is derived, enabling us to describe the set of optimal solutions geometrically. Moreover,
Interior-Point methods are described which yield an $\varepsilon$-optimal solution in polynomial time.
Received: February 1999 / Accepted: March 2002 Published online: September 5, 2002
Key words. Goal programming – closest points – interior point methods – location – regression |
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