naa a22 4500 51080909X CHVBK 20180411083433.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s12532-013-0051-x doi (NATIONALLICENCE)springer-10.1007/s12532-013-0051-x Efficient block-coordinate descent algorithms for the Group Lasso [Elektronische Daten] [Zhiwei Qin, Katya Scheinberg, Donald Goldfarb] We present two algorithms to solve the Group Lasso problem (Yuan and Lin in, J R Stat Soc Ser B (Stat Methodol) 68(1):49-67, 2006). First, we propose a general version of the Block Coordinate Descent (BCD) algorithm for the Group Lasso that employs an efficient approach for optimizing each subproblem exactly. We show that it exhibits excellent performance when the groups are of moderate size. For groups of large size, we propose an extension of ISTA/FISTA SIAM (Beck and Teboulle in, SIAM J Imag Sci 2(1):183-202, 2009) based on variable step-lengths that can be viewed as a simplified version of BCD. By combining the two approaches we obtain an implementation that is very competitive and often outperforms other state-of-the-art approaches for this problem. We show how these methods fit into the globally convergent general block coordinate gradient descent framework in Tseng and Yun (Math Program 117(1):387-423, 2009). We also show that the proposed approach is more efficient in practice than the one implemented in Tseng and Yun (Math Program 117(1):387-423, 2009). In addition, we apply our algorithms to the Multiple Measurement Vector (MMV) recovery problem, which can be viewed as a special case of the Group Lasso problem, and compare their performance to other methods in this particular instance. Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society, 2013 Block coordinate descent nationallicence Group Lasso nationallicence Iterative shrinkage thresholding nationallicence Multiple measurement vector nationallicence Line-search nationallicence Qin Zhiwei Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA aut Scheinberg Katya Department of Industrial and Systems Engineering, Lehigh University, 18015, Bethlehem, PA, USA aut Goldfarb Donald Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA aut Mathematical Programming Computation Springer-Verlag 5/2(2013-06-01), 143-169 1867-2949 5:2<143 2013 5 12532 https://doi.org/10.1007/s12532-013-0051-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12532-013-0051-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Qin Zhiwei Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA aut NATIONALLICENCE 700 1- Scheinberg Katya Department of Industrial and Systems Engineering, Lehigh University, 18015, Bethlehem, PA, USA aut NATIONALLICENCE 700 1- Goldfarb Donald Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA aut NATIONALLICENCE 773 0- Mathematical Programming Computation Springer-Verlag 5/2(2013-06-01), 143-169 1867-2949 5:2<143 2013 5 12532 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer