$\ell_0hBcminimization – Optimization Online

Dual-density-based reweighted $\ell_{1}hBcalgorithms for a class of $\ell_{0}hBcminimization problems

Published: 2019/10/02

Convex and Nonsmooth Optimization $\ell_0hBcminimization, bilevel optimization, convex relaxation, dual-density-based algorithm, merit functions for sparsity, strict complementarity

The optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted $\ell_{1}$-algorithms for a class of $\ell_{0}$-minimization models which can be used to model a wide range of practical problems. This class of … Read more

1-Bit Compressive Sensing: Reformulation and RRSP-Based Sign Recovery Theory

Published: 2016/07/03

Chunlei Xu

Yun-Bin Zhao

Convex Optimization, Data-Mining $\ell_0hBcminimization, 1-bit basis pursuit, compressed sensing, linear programming, restricted range space property, sparse signal recovery

Recently, the 1-bit compressive sensing (1-bit CS) has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. In this paper, we first … Read more

Uniqueness Conditions for A Class of $\ell_0hBcMinimization Problems

Published: 2013/12/19, Updated: 2014/01/30

C Xu

Yun-Bin Zhao

Applications - OR and Management Sciences, Applications - Science and Engineering, Data-Mining $\ell_0hBcminimization, uniqueness condition

We consider a class of $\ell_0$-minimization problems, which is to search for the partial sparsest solution to an underdetermined linear system with additional constraints. We introduce several concepts, including $l_p$-induced quasi-norm ($0