Projected Subgradient Minimization Versus Superiorization

Yair Censor (), Ran Davidi, Gabor T. Herman, Reinhard W. Schulte and Luba Tetruashvili
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Yair Censor: University of Haifa
Ran Davidi: Stanford University
Gabor T. Herman: City University of New York
Reinhard W. Schulte: Loma Linda University Medical Center
Luba Tetruashvili: University of Haifa

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 3, No 2, 730-747

Abstract: Abstract The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to regain feasibility. The latter poses a computational difficulty, and, therefore, the projected subgradient method is applicable only when the feasible region is “simple to project onto.” In contrast to this, in the superiorization methodology a feasibility-seeking algorithm leads the overall process, and objective function steps are interlaced into it. This makes a difference because the feasibility-seeking algorithm employs projections onto the individual constraints sets and not onto the entire feasible region. We present the two approaches side-by-side and demonstrate their performance on a problem of computerized tomography image reconstruction, posed as a constrained minimization problem aiming at finding a constraint-compatible solution that has a reduced value of the total variation of the reconstructed image.

Keywords: Constrained minimization; Feasibility-seeking; Bounded convergence; Superiorization; Projected subgradient method; Proximity function; Strong perturbation resilience; Image reconstruction; Computerized tomography (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-013-0408-3

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