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.

On some steplength approaches for proximal algorithms / Porta, Federica; Loris, Ignace. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 253:(2015), pp. 345-362. [10.1016/j.amc.2014.12.079]

On some steplength approaches for proximal algorithms

PORTA, FEDERICA;Loris, Ignace
2015

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.
2015
253
345
362
On some steplength approaches for proximal algorithms / Porta, Federica; Loris, Ignace. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 253:(2015), pp. 345-362. [10.1016/j.amc.2014.12.079]
Porta, Federica; Loris, Ignace
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1171763
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