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.

优越性方法旨在与受约束的最小化问题（即目标函数和一组约束）的输入数据一起使用。但是，它基于对导致最小化方法受限的对立思想。代替使无约束的最小化算法适应于处理约束，它使寻求可行性的算法适应于减小（不一定最小化）目标函数值。这是通过将减少目标函数的扰动插入到寻求可行性的算法中，同时保留其寻求可行性的能力，而无需付出高昂的计算成本。提出了一种采用逐组分目标函数简化步骤的高级算法。这样可以实现无导数优势（DFS），意味着可以将优势应用于没有可计算的偏导数或次梯度的目标函数。我们的无导数优势算法的数值行为在通过模拟从投影图像重建问题生成的数据集上得到了说明。我们介绍一种工具（我们称其为确定两个迭代方法中的哪一个“更好”解决特定问题的“接近目标曲线”。我们实验的接近目标曲线图展示了所提出的无导数优势算法的优势。