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Poster
Strong NP-Hardness for Sparse Optimization with Concave Penalty Functions
Yichen Chen · Dongdong Ge · Mengdi Wang · Zizhuo Wang · Yinyu Ye · Hao Yin
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 $\mathcal{O}(n^{c_1}d^{c_2})$-optimal solution to the regularized sparse optimization problem is strongly NP-hard for any $c_1, c_2\in [0,1)$ such that $c_1+c_2$ less than 1. We also prove strong NP-hardness results for the sparsity-constrained optimizaiotn problem. These results apply to a broad class of loss functions and sparse penalty functions. They suggest that one cannot even approximately solve the sparse optimization problem in polynomial time, unless P $=$ NP.
Summary/Notes »Author Information
Yichen Chen (Princeton University)
Dongdong Ge (Shanghai University of Finance and Economics)
Mengdi Wang (Princeton University)
Zizhuo Wang (University of Minnesota)
Yinyu Ye
Hao Yin (Stanford University)
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2017 Talk: Strong NP-Hardness for Sparse Optimization with Concave Penalty Functions »
Mon Aug 7th 01:24 -- 01:42 AM Room Parkside 2
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