Bounded perturbation resilience of projected scaled gradient methods

Wenma Jin, Yair Censor () and Ming Jiang

Computational Optimization and Applications, 2016, vol. 63, issue 2, 365-392

Abstract: We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, the projected Landweber-type methods and the generalized expectation-maximization (EM)-type methods. We prove the convergence of the PSG methods in the presence of bounded perturbations. This resilience to bounded perturbations is relevant to the ability to apply the recently developed superiorization methodology to PSG methods, in particular to the EM algorithm. Copyright Springer Science+Business Media New York 2016

Keywords: Convex minimization problems; Proximity function; Projected scaled gradient; Superiorization; Bounded perturbation resilience (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10589-015-9777-x

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