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|Title:||On controlling the parameter in the logarithmic barrier term for convex programming problems|
|Source:||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. https://doi.org/10.1007/BF02191739|
|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|
|Appears in Collections:||Staff Publications|
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