7531
eng
reportzib
0
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2019-11-30
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Linear Programming using Limited-Precision Oracles
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations is considered through a bit-complexity analysis. Yet in practice, implementations typically use limited-precision arithmetic. In this paper we introduce the idea of a limited-precision LP oracle and study how such an oracle could be used within a larger framework to compute exact precision solutions to LPs. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. This work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.
1438-0064
10.1007/s10107-019-01444-6
urn:nbn:de:0297-zib-75316
Mathematical Programming, 2019
false
true
Ambros Gleixner
Ambros Gleixner
Daniel Steffy
ZIB-Report
19-57
Mathematical Optimization
Mathematical Optimization Methods
Gleixner, Ambros
MIP-ZIBOPT
MODAL-SynLab
MODAL-Gesamt
https://opus4.kobv.de/opus4-zib/files/7531/ZR-19-57.pdf