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Strong NP-Hardness for Sparse Optimization with Concave Penalty Functions

2020-03-09 | |  60 |   34 |   0

Abstract

Consider the regularized sparse minimization problem, which involves empirical sums of loss functions for n data points (each of dimension d) and a nonconvex sparsity penalty. We prove that finding an 图片.png-optimal solution to the regularized sparse optimization problem is strongly NP-hard for any 图片.png such tha 图片.png The result applies to a broad class of loss functions and sparse penalty functions. It suggests that one cannot even approximately solve the sparse optimization problem in polynomial time, unless P = NP.

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