On controlling the parameter in the logarithmic barrier term for convex programming problems

K. O Kortanek; J Zhu

doi:10.1007/BF02191739

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On controlling the parameter in the logarithmic barrier term for convex programming problems

Journal article

Peer reviewed

On controlling the parameter in the logarithmic barrier term for convex programming problems

K. O Kortanek and J Zhu

Journal of optimization theory and applications, Vol.84(1), pp.117-143

1995

DOI: 10.1007/BF02191739

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Abstract

We present a log-barrier based algorithm for linearly constrained convex differentiable programming problems in nonnegative variables, but where the objective function may not be differentiable at points having a zero coordinate. We use an approximate centering condition as a basis for decreasing the positive parameter of the log-barrier term and show that the total number of iterations to achieve an ε-tolerance optimal solution isO(|log(ε)|)×(number of inner-loop iterations). When applied to then-variable dual geometric programming problem, this bound becomesO(n 2 U/ε), whereU is an upper bound on the maximum magnitude of the iterates generated during the computation.

Applied Sciences

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Mathematical programming

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Operational research. Management science

Details

Title: Subtitle: On controlling the parameter in the logarithmic barrier term for convex programming problems
Creators: K. O Kortanek - University of Iowa
J Zhu - National University of Singapore
Resource Type: Journal article
Publication Details: Journal of optimization theory and applications, Vol.84(1), pp.117-143
DOI: 10.1007/BF02191739
ISSN: 0022-3239
eISSN: 1573-2878
Publisher: Springer
Number of pages: 27
Language: English
Date published: 1995
Academic Unit: Business Analytics
Record Identifier: 9984963218302771

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