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Title: Exterior point simplex-type algorithms for linear and network optimization problems
Authors: Paparrizos, Konstantinos
Samaras, Nikolaos
Sifaleras, Angelo
Type: Article
Subjects: FRASCATI::Natural sciences::Mathematics::Applied Mathematics
FRASCATI::Natural sciences::Computer and information sciences
Keywords: Mathematical programming
Exterior point simplex-type algorithms
Linear programming
Network flows
Issue Date: 2015
Publisher: Springer
Source: Annals of Operations Research
Volume: 229
Issue: 1
First Page: 607
Last Page: 633
Abstract: Two decades of research led to the development of a number of efficient algorithms that can be classified as exterior point simplex-type. This type of algorithms can cross over the infeasible region of the primal (dual) problem and find an optimal solution reducing the number of iterations needed. The main idea of exterior point simplex-type algorithms is to compute two paths/flows. Primal (dual) exterior point simplex-type algorithms compute one path/flow which is basic but not always primal (dual) feasible and the other is primal (dual) feasible but not always basic. The aim of this paper is to explain to the general OR audience, for the first time, the developments in exterior point simplex-type algorithms for linear and network optimization problems, over the recent years. We also present other approaches that, in a similar way, do not preserve primal or dual feasibility at each iteration such as the monotonic build-up Simplex algorithms and the criss-cross methods.
ISSN: 0254-5330
Other Identifiers: 10.1007/s10479-014-1769-1
Appears in Collections:Department of Applied Informatics

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