Proximal gradient method: Difference between revisions

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{{more footnotes|date=November 2013}}

'''Proximal gradient methods''' are a generalized form of projection used to solve non-differentiable [[convex optimization]] problems. Many interesting problems can be formulated as convex optimization problems of form

:<math>

\operatorname{min}\limits_{x \in \mathbb{R}^N} f_1(x) +f_2(x) + \cdots+ f_sum_{n-i=1}(x)^n +f_nf_i(x)

</math>

where <math>f_1f_i,\ f_2,i ...= 1, f_n\dots, n</math> are [[convex functions]] defined from <math>f: \mathbb{R}^N \rightarrow \mathbb{R} </math>

where <math>f_1, f_2, ..., f_n </math> are [[convex functions]] defined from <math>f: \mathbb{R}^N \rightarrow \mathbb{R} </math>

where some of the functions are non-differentiable, this rules out our conventional smooth optimization techniques like

[[Gradient descent|Steepest descent method]], [[conjugate gradient method]] etc. There is a specific class of [[algorithms]] which can solve the above optimization problem. These methods proceed by splitting,