A double smoothing technique for solving unconstrained nondifferentiable\n convex optimization problems

2012/03/09 by Radu Ioan Boţ, Radu Ioan Bot, Bot, Radu Ioan +2 · 1 voice
Computer Science · Engineering · Mathematics · #47A52 #90C25 #90C46 #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques #math.OC

paper · pdf · doi:10.48550/arxiv.1203.2070

openalex publication_date 2012/03/09 · arxiv published 2012/03/09 · arxiv updated 2012/03/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to develop an efficient algorithm for solving a\nclass of unconstrained nondifferentiable convex optimization problems in finite\ndimensional spaces. To this end we formulate first its Fenchel dual problem and\nregularize it in two steps into a differentiable strongly convex one with\nLipschitz continuous gradient. The doubly regularized dual problem is then\nsolved via a fast gradient method with the aim of accelerating the resulting\nconvergence scheme. The theoretical results are finally applied to an l1\nregularization problem arising in image processing.\n

Citations

• Smooth minimization of non-smooth functions

Discussions

• Motivation . Consider the problem of finding a minimizer $x$ of a convex function $J(x)$ . The trust region method generates iterates by solving, at each step, a norm-constrained quadratic minimizatio [stackexchange, 3 points]

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