Generalized Goal Programming: Polynomial Methods and Applications

Emilio Carrizosa (ecarrizcica.es)
Joerg Fliege (fliegemath.uni-dortmund.de)

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.

Keywords: Goal Programming, Closest points, Interior point methods, Location, Regression.

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Applications -- OR and Management Sciences (Other )

Citation: UNPUBLISHED. INSTITUTION = {Vakgroep Beleidsinformatica, Department of Management Informatics, Vrije Universiteit Brussel}, YEAR = 1999, NUMBER = {BEIF/108}, ADDRESS = {Pleinlaan 2, B-1050 Brussel, Belgium}, MONTH = {January}

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Entry Submitted: 01/19/2001
Entry Accepted: 01/19/2001
Entry Last Modified: 01/19/2001

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