Superiorization with level control. (1st March 2017)
- Record Type:
- Journal Article
- Title:
- Superiorization with level control. (1st March 2017)
- Main Title:
- Superiorization with level control
- Authors:
- Cegielski, Andrzej
Al-Musallam, Fadhel - Abstract:
- Abstract: The convex feasibility problem is to find a common point of a finite family of closed convex subsets. In many applications one requires something more, namely finding a common point of closed convex subsets which minimizes a continuous convex function. The latter requirement leads to an application of the superiorization methodology which is actually settled between methods for convex feasibility problem and the convex constrained minimization. Inspired by the superiorization idea we introduce a method which sequentially applies a long-step algorithm for a sequence of convex feasibility problems; the method employs quasi-nonexpansive operators as well as subgradient projections with level control and does not require evaluation of the metric projection. We replace a perturbation of the iterations (applied in the superiorization methodology) by a perturbation of the current level in minimizing the objective function. We consider the method in the Euclidean space in order to guarantee the strong convergence, although the method is well defined in a Hilbert space.
- Is Part Of:
- Inverse problems. Volume 33:Number 4(2017:Apr.)
- Journal:
- Inverse problems
- Issue:
- Volume 33:Number 4(2017:Apr.)
- Issue Display:
- Volume 33, Issue 4 (2017)
- Year:
- 2017
- Volume:
- 33
- Issue:
- 4
- Issue Sort Value:
- 2017-0033-0004-0000
- Page Start:
- Page End:
- Publication Date:
- 2017-03-01
- Subjects:
- convex minimization -- convex feasibility problem -- superiorization -- quasi-nonexpansive operator -- subgradient projection
Inverse problems (Differential equations) -- Periodicals
515.357 - Journal URLs:
- http://iopscience.iop.org/0266-5611 ↗
http://ioppublishing.org/ ↗ - DOI:
- 10.1088/1361-6420/aa5d79 ↗
- Languages:
- English
- ISSNs:
- 0266-5611
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - BLDSS-3PM
British Library STI - ELD Digital store - Ingest File:
- 8446.xml