Derivative-free superiorization: principle and algorithm

The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained minimization methods. Instead of adapting unconstrained min...

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Veröffentlicht in:Numerical algorithms Jg. 88; H. 1; S. 227 - 248
Hauptverfasser: Censor, Yair, Garduño, Edgar, Helou, Elias S., Herman, Gabor T.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2021
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Bibliographic literature
Computer Science
Constraints
Derivatives
Feasibility
Image reconstruction
Inverse problems
Iterative methods
Mathematical analysis
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Radiation therapy
Theory of Computation
Variables
65K15
Constrained minimization
65K05
Component-wise perturbations
90C56
Bounded perturbations
Regularization
Superiorization
Proximity function
Derivative-free
ISSN:1017-1398, 1572-9265
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Zusammenfassung:The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained minimization methods. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce (not necessarily minimize) target function values. This is done by inserting target-function-reducing perturbations into a feasibility-seeking algorithm while retaining its feasibility-seeking ability and without paying a high computational price. A superiorized algorithm that employs component-wise target function reduction steps is presented. This enables derivative-free superiorization (DFS), meaning that superiorization can be applied to target functions that have no calculable partial derivatives or subgradients. The numerical behavior of our derivative-free superiorization algorithm is illustrated on a data set generated by simulating a problem of image reconstruction from projections. We present a tool (we call it a proximity-target curve ) for deciding which of two iterative methods is “better” for solving a particular problem. The plots of proximity-target curves of our experiments demonstrate the advantage of the proposed derivative-free superiorization algorithm.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-01038-w