The randomized subspace Newton convex methods for the sensor selection problem are proposed. The randomized subspace Newton algorithm is straightforwardly applied to the convex formulation, and the customized method in which the half of the update variables are selected to be the present best sensor candidates is also considered. In the converged solution, almost the same results are obtained by original and randomized-subspace-Newton convex methods. As expected, the randomized-subspace-Newton methods require more computational steps while they reduce the total amount of the computational time because the computational time for one step is significantly reduced by the cubic of the ratio of numbers of randomly updating variables to all the variables. The customized method shows superior performance to the straightforward implementation in terms of the quality of sensors and the computational time.

中文翻译：

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随机子空间牛顿凸方法应用于数据驱动的传感器选择问题

提出了传感器选择问题的随机子空间牛顿凸方法。随机子空间牛顿算法直接应用于凸公式，并且还考虑了其​​中一半更新变量被选择为当前最佳传感器候选者的定制方法。在收敛解中，原始方法和随机子空间牛顿凸方法获得几乎相同的结果。正如预期的那样，随机子空间牛顿方法需要更多的计算步骤，同时它们减少了计算时间的总量，因为一步的计算时间显着减少了随机更新变量数与所有变量数之比的三次方.