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1295. Mix Sparse Optimization: Theory and Algorithm

Invited abstract in session TD-41: Lower-order composite optimization problems, stream Nonsmooth Optimization.

Tuesday, 14:30-16:00
Room: 97 (building: 306)

Authors (first author is the speaker)

1.	Xiaoqi Yang
	Department of Applied Mathematics, The Hong Kong Polytechnic University

Abstract

In this talk, we consider the $\ell_0$ regularization problem for mix sparse optimization and investigate its mathematical theory and algorithm. In the theoretical part, we first introduce the notions of sparse eigenvalue conditions, one of the weakest regularity conditions in the literature, and then establish the oracle property without any regularity condition and provide a recovery bound for the mix sparse optimization problem under the weak assumption of sparse eigenvalue condition. Moreover, an asymptotic analysis is provided to advance the understanding of the convergence of the $\ell_p$ regularization to the $\ell_0$ regularization. In the algorithmic part, we propose an iterative mix thresholding algorithm with continuation technique (IMTC) to solve the mix sparse optimization problem and present its global convergence theorem and linear convergence rate to a local minimum. The significant advantage of the IMTC is that it has a closed-form expression and low storage requirement, and promotes the mix sparse structure of the solution. Numerical results on simulated data indicate that the IMTC has a strong promoting capability of the mix sparse structure and outperforms

Keywords

• Non-smooth Optimization
• Machine Learning
• Continuous Optimization

Status: accepted

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