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.
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Communicated by A. V. Fiacco
The authors gratefully acknowledge very constructive and insightful comments and suggestions from the two anonymous referees and the correspondence from A. V. Fiacco (Ref. 1).
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Kortanek, K.O., Zhu, J. On controlling the parameter in the logarithmic barrier term for convex programming problems. J Optim Theory Appl 84, 117–143 (1995). https://doi.org/10.1007/BF02191739
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DOI: https://doi.org/10.1007/BF02191739