Title | Bounded perturbation resilience of projected scaled gradient methods |
Authors | Jin, Wenma Censor, Yair Jiang, Ming |
Affiliation | Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China. Univ Haifa, Dept Math, IL-3498838 Haifa, Israel. Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China. Shanghai Jiao Tong Univ, Cooperat Medianet Innovat Ctr, Shanghai 200240, Peoples R China. |
Keywords | Convex minimization problems Proximity function Projected scaled gradient Superiorization Bounded perturbation resilience LINEAR COMPLEMENTARITY-PROBLEM ITERATIVE IMAGE-RECONSTRUCTION MATRIX SPLITTING ALGORITHM EM ALGORITHM OPTIMIZATION PROBLEMS FEASIBILITY PROBLEMS CONVERGENCE ANALYSIS CONVEX-OPTIMIZATION DESCENT METHODS LEAST-SQUARES |
Issue Date | 2016 |
Publisher | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS |
Citation | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS.2016,63,(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. |
URI | http://hdl.handle.net/20.500.11897/437590 |
ISSN | 0926-6003 |
DOI | 10.1007/s10589-015-9777-x |
Indexed | SCI(E) EI |
Appears in Collections: | 数学科学学院 北京国际数学研究中心 数学及其应用教育部重点实验室 |