Performance of first- and second-order methods for -regularized least squares problems

被引：0
|
作者：
Fountoulakis, Kimon [1 ,2 ]
Gondzio, Jacek [1 ,2 ,3 ]
机构：
[1] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland
[2] Univ Edinburgh, Maxwell Inst, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland
[3] NASK Res Inst, Wawozowa 18, PL-02796 Warsaw, Poland
来源：
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2016年 / 65卷 / 03期
关键词：
l(1)-Regularised least-squares; First-order methods; Second-order methods; Sparse least squares instance generator; Ill-conditioned problems; COORDINATE DESCENT METHOD; OPTIMIZATION; MINIMIZATION; CONVERGENCE; ALGORITHM;
D O I：
10.1007/s10589-016-9853-x
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We study the performance of first- and second-order optimization methods for -regularized sparse least-squares problems as the conditioning of the problem changes and the dimensions of the problem increase up to one trillion. A rigorously defined generator is presented which allows control of the dimensions, the conditioning and the sparsity of the problem. The generator has very low memory requirements and scales well with the dimensions of the problem.
引用
收藏
页码：605 / 635
页数：31
相关论文
共 50 条
  • [1] Least-squares for second-order elliptic problems
    Bramble, JH
    Lazarov, RD
    Pasciak, JE
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 152 (1-2) : 195 - 210
  • [2] First- and second-order methods for semidefinite programming
    Renato. D. C. Monteiro
    Mathematical Programming, 2003, 97 : 209 - 244
  • [3] First- and second-order methods for semidefinite programming
    Monteiro, RDC
    MATHEMATICAL PROGRAMMING, 2003, 97 (1-2) : 209 - 244
  • [4] SEMIDISCRETE LEAST-SQUARES METHODS FOR SECOND-ORDER PARABOLIC PROBLEMS WITH NONHOMOGENOUS DATA
    KING, JT
    MATHEMATICS OF COMPUTATION, 1974, 28 (126) : 405 - 411
  • [5] Gaslighting, First- and Second-Order
    Catapang Podosky, Paul-Mikhail
    HYPATIA-A JOURNAL OF FEMINIST PHILOSOPHY, 2021, 36 (01): : 207 - 227
  • [6] Noise robust phonetic classification with linear regularized least squares and second-order features
    Rifkin, Ryan
    Schutte, Ken
    Saad, Michelle
    Bouvrie, Jake
    Glass, Jim
    2007 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOL IV, PTS 1-3, 2007, : 881 - +
  • [7] Regularized BIE formulations for first- and second-order shape sensitivity of elastic fields
    Bonnet, M.
    Computers and Structures, 1995, 56 (05): : 799 - 811
  • [8] Least-squares mixed method for second-order elliptic problems
    Kim, Y
    Lee, S
    APPLIED MATHEMATICS AND COMPUTATION, 2000, 115 (2-3) : 89 - 100
  • [9] Almost periodic solutions of first- and second-order Cauchy problems
    Arendt, W
    Batty, CJK
    JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 137 (02) : 363 - 383
  • [10] First- and Second-Order Methods for Online Convolutional Dictionary Learning
    Liu, Jialin
    Garcia-Cardona, Cristina
    Wohlbereg, Brendt
    Yin, Wotao
    SIAM JOURNAL ON IMAGING SCIENCES, 2018, 11 (02): : 1589 - 1628
12345