Superiorization reduces, not necessarily minimizes, the value of a target function while seeking constraints compatibility. This is done by taking a solely feasibility-seeking algorithm, analyzing its perturbation resilience, and proactively perturbing its iterates accordingly to steer them toward a feasible point with reduced value of the target function. When the perturbation steps are computationally efficient, this enables generation of a superior result with essentially the same computational cost as that of the original feasibility-seeking algorithm. In this work, we refine previous formulations of the superiorization method to create a more general framework, enabling target function reduction steps that do not require partial derivatives of the target function. In perturbations that use partial derivatives, the step-sizes in the perturbation phase of the superiorization method are chosen independently from the choice of the nonascent directions. This is no longer true when component-wise perturbations are employed. In that case, the step-sizes must be linked to the choice of the nonascent direction in every step. Besides presenting and validating these notions, we give a computational demonstration of superiorization with component-wise perturbations for a problem of computerized tomography image reconstruction.

中文翻译：

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无导数的优越性与按组件的扰动。

在寻求约束兼容性时，优势降低了目标功能的价值，而未必会使其最小化。这是通过采用仅寻求可行性的算法，分析其摄动弹性并相应地主动摄制其迭代来完成的，从而将其引向目标函数值降低的可行点。当扰动步骤在计算上是有效的时，这使得能够产生与原始的寻求可行性的算法基本相同的计算成本的优异结果。在这项工作中，我们改进了优势方法的先前公式，以创建一个更通用的框架，从而实现了目标函数简化步骤，而这些步骤不需要目标函数的偏导数。在使用偏导数的摄动中，优越方法的扰动阶段中的步长大小独立于非上升方向的选择来选择。当采用逐分量摄动时，这不再成立。在这种情况下，步长必须与每个步骤中非上升方向的选择相关联。除了提出和验证这些概念外，我们还针对计算机断层图像重建问题给出了基于分量摄动的优越性的计算演示。