Proximal gradient methods for learning: Difference between revisions

Revision as of 08:07, 16 August 2014

Revision as of 18:29, 16 December 2014

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== Relevant background ==

[[Proximal Gradient Methods|Proximal gradient methodsmethod]]s are applicable in a wide variety of scenarios for solving [[convex optimization]] problems of the form

:<math> \min_{x\in \mathcal{H}} F(x)+R(x),</math>

where <math>F</math> is [[Convex function|convex]] and differentiable with [[Lipschitz continuity|Lipschitz continuous]] [[gradient]], <math> R</math> is a [[Convex function|convex]], [[Semicontinuous function|lower semicontinuous]] function which is possibly nondifferentiable, and <math>\mathcal{H}</math> is some set, typically a [[Hilbert space]]. The usual criterion of <math> x</math> minimizes <math> F(x)+R(x)</math> if and only if <math> \nabla (F+R)(x) = 0</math> in the convex, differentiable setting is now replaced by