On some steplength approaches for proximal algorithms

Federica Porta and Ignace Loris

Applied Mathematics and Computation, 2015, vol. 253, issue C, 345-362

Abstract: We discuss a number of novel steplength selection schemes for proximal-based convex optimization algorithms. In particular, we consider the problem where the Lipschitz constant of the gradient of the smooth part of the objective function is unknown. We generalize two optimization algorithms of Khobotov type and prove convergence. We also take into account possible inaccurate computation of the proximal operator of the non-smooth part of the objective function. Secondly, we show convergence of an iterative algorithm with Armijo-type steplength rule, and discuss its use with an approximate computation of the proximal operator. Numerical experiments show the efficiency of the methods in comparison to some existing schemes.

Keywords: Proximal algorithms; Steplength selection; Non-smooth optimization; Signal recovering (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:253:y:2015:i:c:p:345-362

DOI: 10.1016/j.amc.2014.12.079

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