This paper focuses on designing a unified approach for computing the projection onto the intersection of a one-norm ball or sphere and a two-norm ball or sphere. We show that the solutions of these problems can all be determined by the root of the same piecewise quadratic function. We make use of the special structure of the auxiliary function and propose a novel bisection algorithm with finite termination. We show that the proposed method possesses quadratic time worst-case complexity. The efficiency of the proposed algorithm is demonstrated in numerical experiments, which show the proposed method has linear time complexity in practice.

中文翻译：

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投影到一范数球或球体与二范数球或球体的交点

本文侧重于设计一种统一的方法来计算单范数球或球体与二范数球或球体的交集的投影。我们表明这些问题的解都可以由同一个分段二次函数的根确定。我们利用辅助函数的特殊结构，提出了一种新的有限终止二分算法。我们表明所提出的方法具有二次时间最坏情况复杂度。数值实验证明了该算法的有效性，表明该算法在实践中具有线性时间复杂度。