Bounded perturbation resilience of projected scaled gradient methods

Wenma Jin, Yair Censor, Ming Jiang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)365-392
Number of pages28
JournalComputational Optimization and Applications
Issue number2
StatePublished - 1 Mar 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media New York.


  • Bounded perturbation resilience
  • Convex minimization problems
  • Projected scaled gradient
  • Proximity function
  • Superiorization

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


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