A strongly polynomial-time algorithm for the strict homogeneous linear-inequality feasibility problem

A strongly polynomial-time algorithm is proposed for the strict homogeneous linear-inequality feasibility problem in the positive orthant, that is, to obtain x ∈ R n , such that A x > 0 , x > 0 , for an m × n matrix A , m ≥ n . This algorithm requires O ( p ) iterations and O ( m 2 ( n + p ) )...

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Veröffentlicht in:Mathematical methods of operations research (Heidelberg, Germany) Jg. 80; H. 3; S. 267 - 284
1. Verfasser: Oliveira, Paulo Roberto
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2014
Springer Nature B.V
Schlagworte:
Algorithms
Business and Management
Calculus of Variations and Optimal Control; Optimization
Feasibility
Inversions
Iterative methods
Linear programming
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Operations research
Operations Research/Decision Theory
Original Article
Polynomials
Studies
Texts
Strict linear-inequality feasibility
15A39
Linear programming
49M15
Strong polynomial method
Application of non-linear programming to feasibility problems
ISSN:1432-2994, 1432-5217
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Zusammenfassung:A strongly polynomial-time algorithm is proposed for the strict homogeneous linear-inequality feasibility problem in the positive orthant, that is, to obtain x ∈ R n , such that A x > 0 , x > 0 , for an m × n matrix A , m ≥ n . This algorithm requires O ( p ) iterations and O ( m 2 ( n + p ) ) arithmetical operations to ensure that the distance between the solution and the iteration is 10 - p . No matrix inversion is needed. An extension to the non-homogeneous linear feasibility problem is presented.
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ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-014-0480-y