Fast first-order methods for convex optimization with line search
published: Jan. 25, 2012, recorded: December 2011, views: 5012
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We propose accelerated first-order methods with non-monotonic choice of the prox parameter, which essentially controls the step size. This is in contrast with most accelerated schemes where the prox parameter is either assumed to be constant or non-increasing. In particular we show that a backtracking strategy can be used within FISTA  and FALM algorithms  starting from an arbitrary parameter value preserving their worst-case iteration complexities of O. We also derive complexity estimates that depend on the “average” step size rather than the global Lipschitz constant for the function gradient, which provide better theoretical justification for these methods, hence the main contribution of this paper is theoretical.
Download slides: nipsworkshops2011_scheinberg_convexoptimization_01.pdf (2.3 MB)
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