General Polynomial Time Decomposition Algorithms

9 years 27 days ago
General Polynomial Time Decomposition Algorithms
We present a general decomposition algorithm that is uniformly applicable to every (suitably normalized) instance of Convex Quadratic Optimization and efficiently approaches an optimal solution. The number of iterations required to be within ε of optimality grows linearly with 1/ε and quadratically with the number m of variables. The working set selection can be performed in polynomial time. If we restrict our considerations to instances of Convex Quadratic Optimization with at most k0 equality constraints for some fixed constant k0 plus some so-called box-constraints (conditions that hold for most variants of SVM-optimization), the working set is found in linear time. Our analysis builds on a generalization of the concept of rate certifying pairs that was introduced by Hush and Scovel. In order to extend their results to arbitrary instances of Convex Quadratic Optimization, we introduce the general notion of a rate certifying q-set. We improve on the results by Hush and Scovel (2...
Nikolas List, Hans-Ulrich Simon
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where COLT
Authors Nikolas List, Hans-Ulrich Simon
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