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On Lower Complexity Bounds for Large-Scale Smooth Convex Optimization

Cristobal Guzman(cguzman***at***gatech.edu)
Arkadi Nemirovski(arkadi.nemirovski***at***isye.gatech.edu)

Abstract: In this note we present tight lower bounds on the information-based complexity of large-scale smooth convex minimization problems. We demonstrate, in particular, that the k-step Conditional Gradient (a.k.a. Frank-Wolfe) algorithm as applied to minimizing smooth convex functions over the n-dimensional box with n ≥ k is optimal, up to an O(ln n)-factor, in terms of information-based complexity.

Keywords: Oracle Complexity, First Order Methods, Smooth Convex Programming, Conditional Gradient Method

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Convex and Nonsmooth Optimization (Other )

Citation:

Download: [PDF]

Entry Submitted: 07/18/2013
Entry Accepted: 07/18/2013
Entry Last Modified: 07/18/2013

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