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Title: On controlling the parameter in the logarithmic barrier term for convex programming problems
Authors: Kortanek, K.O.
Zhu, J. 
Keywords: barrier methods
Convex programming
geometric programming
interior-point methods
linear constraints
Issue Date: Jan-1995
Citation: Kortanek, K.O., Zhu, J. (1995-01). On controlling the parameter in the logarithmic barrier term for convex programming problems. Journal of Optimization Theory and Applications 84 (1) : 117-143. ScholarBank@NUS Repository.
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 is O(|log(ε)|)×(number of inner-loop iterations). When applied to the n-variable dual geometric programming problem, this bound becomes O(n2U/ε), where U is an upper bound on the maximum magnitude of the iterates generated during the computation. © 1995 Plenum Publishing Corporation.
Source Title: Journal of Optimization Theory and Applications
ISSN: 00223239
DOI: 10.1007/BF02191739
Appears in Collections:Staff Publications

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