Complexity of Convex Optimization Using Geometry-Based Measures and a Reference Point (2002)
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@MISC{Freund02complexityof,
author = {Robert M. Freund},
title = {Complexity of Convex Optimization Using Geometry-Based Measures and a Reference Point},
year = {2002}
}
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Abstract
Our concern lies in solving the following convex optimization problem: G P : minimize x c where P is a closed convex subset of the n-dimensional vector space X. We bound the complexity of computing an almost-optimal solution of G P in terms of natural geometry-based measures of the feasible region and the level-set of almost-optimal solutions, relative to a given that might be close to the feasible region and/or the almost-optimal level set. This contrasts with other complexity bounds for convex optimization that rely on data-based condition numbers or algebraic measures, and that do not take into account any a priori reference point information. AMS Subject Classification: 90C, 90C05, 90C60 Keywords: Convex Optimization, Complexity, Interior-Point Method, Barrier Method This research has been partially supported through the Singapore-MIT Alliance. Portions of this research were undertaken when the author was a Visiting Scientist at Delft University of Technology.
