IMRO swMATH ID: 20465 Software Authors: Karimi, Sahar; Vavasis, Stephen Description: IMRO: A proximal quasi-Newton method for solving ℓ 1 -regularized least squares problems. We present a proximal quasi-Newton method in which the approximation of the Hessian has the special format of “identity minus rank one” (IMRO) in each iteration. The proposed structure enables us to effectively recover the proximal point. The algorithm is applied to \(ell_1\)-regularized least squares problems arising in many applications including sparse recovery in compressive sensing, machine learning, and statistics. Our numerical experiment suggests that the proposed technique competes favorably with other state-of-the-art solvers for this class of problems. We also provide a complexity analysis for variants of IMRO, showing that it matches known best bounds. Homepage: https://arxiv.org/abs/1401.4220 Keywords: proximal methods; quasi-Newton methods; sparse recovery; basis pursuit denoising problem; \(ell_1\)-regularized least squares problem; convex optimization; minimization of composite functions Related Software: NNLS; FPC_AS; TFOCS; TwIST; UNLocBoX; LBFGS-B; UCI-ml; L-BFGS; L1TestPack; SpaSM; Python; MNIST; Saga; SDPNAL+; QUIC; glasso; NewtonLib; SDPT3; iPiano; L-BFGS-B Cited in: 12 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year IMRO: A proximal quasi-Newton method for solving \(\ell_1\)-regularized least squares problems. Zbl 1365.90202Karimi, Sahar; Vavasis, Stephen 2017 all top 5 Cited by 30 Authors 2 Cheng, Wanyou 2 Ochs, Peter 1 Absil, Pierre-Antoine 1 Becker, Stephen R. 1 Dai, Yu-Hong 1 Fadili, Jalal M. 1 Fountoulakis, Kimon 1 Friedlander, Michael P. 1 Goh, Gabriel 1 Goh, Yong Kheng 1 Hu, Qingjie 1 Huang, Wen 1 Jiang, Rujun 1 Karimi, Sahar 1 Leong, Wah June 1 Li, Donghui 1 Liang, Ling 1 Liu, Tianxiang 1 Pock, Thomas 1 Si, Wutao 1 Sim, Hong Seng 1 Takeda, Akiko 1 Tappenden, Rachael 1 Toh, Kim Chuan 1 Tran Dinh Quoc 1 Vary, Simon 1 Vavasis, Stephen A. 1 Wang, Xiaoyu 1 Woo, Gillian Yi Han 1 Yuan, Ya-xiang all top 5 Cited in 7 Serials 4 SIAM Journal on Optimization 2 Computational Optimization and Applications 2 Optimization Methods & Software 1 Journal of the Franklin Institute 1 Mathematics of Operations Research 1 Applied and Computational Harmonic Analysis 1 ETNA. Electronic Transactions on Numerical Analysis Cited in 5 Fields 11 Operations research, mathematical programming (90-XX) 7 Numerical analysis (65-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 1 Operator theory (47-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year