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.
Bibliographical noteFunding Information:
We greatly appreciate the constructive comments of two anonymous reviewers and the Coordinating Editor which helped us improve the paper. This work was supported in part by the National Basic Research Program of China (973 Program) (2011CB809105), the National Science Foundation of China (61421062) and the United States-Israel Binational Science Foundation (BSF) Grant number 2013003.
© 2015, Springer Science+Business Media New York.
- Bounded perturbation resilience
- Convex minimization problems
- Projected scaled gradient
- Proximity function
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Applied Mathematics