Optimization Online


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 )


Download: [PDF]

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

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society