Derivative-free superiorization: principle and algorithm

被引:5
|
作者
Censor, Yair [1 ]
Garduno, Edgar [2 ]
Helou, Elias S. [3 ]
Herman, Gabor T. [4 ]
机构
[1] Univ Haifa, Dept Math, IL-3498838 Haifa, Israel
[2] Univ Nacl Autonoma Mexico, Inst Invest Matemat Aplicadas & Sistemas, Dept Ciencias Comp, Mexico City 04510, DF, Mexico
[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Carlos, SP, Brazil
[4] CUNY, Grad Ctr, Comp Sci PhD Program, New York, NY 10016 USA
关键词
Derivative-free; Superiorization; Constrained minimization; Component-wise perturbations; Proximity function; Bounded perturbations; Regularization; OPTIMIZATION;
D O I
10.1007/s11075-020-01038-w
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:227 / 248
页数:22
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