Improved algorithms for convex minimization in relative scale

Richtárik, Peter
(2011) SIAM Journal on Optimization — Vol. 21, n° 3, p. 1141-1167 (2011)

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  • Richtárik, PeterUCLouvain
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Abstract
In this paper we propose two modifications to Nesterov's algorithms for minimizing convex functions in relative scale. The first is based on a bisection technique and leads to improved theoretical iteration complexity, and the second is a heuristic for avoiding restarting behavior. The fastest of our algorithms produces a solution within relative error O(1/k) of the optimum, with k being the iteration counter. © 2011 Society for Industrial and Applied Mathematics.
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Richtárik, P. (2011). Improved algorithms for convex minimization in relative scale. SIAM Journal on Optimization, 21(3), 1141-1167. https://doi.org/10.1137/090747142 (Original work published 2011)