Method of nonsmooth penalty functions and the theory of extremum problems in Banach space

V. V. Beresnev

doi:10.1007/bf01071224

Method of nonsmooth penalty functions and the theory of extremum problems in Banach space

Cybernetics ◽

10.1007/bf01071224 ◽

1980 ◽

Vol 15 (5) ◽

pp. 712-718 ◽

Cited By ~ 1

Author(s):

V. V. Beresnev

Keyword(s):

Banach Space ◽

Penalty Functions ◽

Extremum Problems ◽

Nonsmooth Penalty

Lassoing eigenvalues

Biometrika ◽

10.1093/biomet/asz076 ◽

2020 ◽

Vol 107 (2) ◽

pp. 397-414 ◽

Cited By ~ 1

Author(s):

David E Tyler ◽

Mengxi Yi

Keyword(s):

Covariance Matrix ◽

Penalty Function ◽

Covariance Matrices ◽

Penalty Functions ◽

Sample Covariance Matrix ◽

Sample Covariance Matrices ◽

Sample Covariance ◽

Nonsmooth Penalty

Summary The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

Modified gradient method for minimization of nonsmooth penalty functions

Journal of Mathematical Sciences ◽

10.1007/bf02114049 ◽

1994 ◽

Vol 71 (5) ◽

pp. 2712-2715

Author(s):

Yu. M. Danilin ◽

D. Numazarov

Keyword(s):

Gradient Method ◽

Penalty Functions ◽

Nonsmooth Penalty

Nonsmooth Penalty Functions

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)39644-1 ◽

2000 ◽

Vol 33 (16) ◽

pp. 287-291

Author(s):

Lyudmila N. Polyakova

Keyword(s):

Penalty Functions ◽

Nonsmooth Penalty

Gradient-based Regularization Parameter Selection for Problems With Nonsmooth Penalty Functions

Journal of Computational and Graphical Statistics ◽

10.1080/10618600.2017.1390470 ◽

2018 ◽

Vol 27 (2) ◽

pp. 426-435 ◽

Cited By ~ 6

Author(s):

Jean Feng ◽

Noah Simon

Keyword(s):

Regularization Parameter ◽

Parameter Selection ◽

Penalty Functions ◽

Gradient Based ◽

Selection For ◽

Nonsmooth Penalty ◽

Regularization Parameter Selection

Gradient-type method for minimization of nonsmooth penalty functions

Cybernetics ◽

10.1007/bf01070592 ◽

1989 ◽

Vol 24 (4) ◽

pp. 511-524

Author(s):

Yu. M. Danilin

Keyword(s):

Penalty Functions ◽

Type Method ◽

Gradient Type ◽

Nonsmooth Penalty

TRANSFORMS, DIFFERENTIAL SUBORDINATIONS AND A p -WEIGHTED INEQUALITIES FOR BANACH-SPACE-VALUED REGULAR MARTINGALES

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30204-2 ◽

1993 ◽

Vol 13 (2) ◽

pp. 180-187

Author(s):

Peide Liu ◽

Youliang Hou

Keyword(s):

Banach Space ◽

Weighted Inequalities ◽

Differential Subordinations

ON FULLY CONVEX AND LOCALLY FULLY CONVEX BANACH SPACE

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30406-5 ◽

1990 ◽

Vol 10 (3) ◽

pp. 327-343 ◽

Cited By ~ 1

Author(s):

Qiyuan Na

Keyword(s):

Banach Space ◽

Convex Banach Space

Three Kinds of Numerical Indices of a Banach Space

Mathematical Proceedings of the Royal Irish Academy ◽

10.3318/pria.2012.112.4 ◽

2012 ◽

Vol 112 (1) ◽

pp. 21-35 ◽

Cited By ~ 1

Author(s):

Sung Guen Kim

Keyword(s):

Banach Space

Unique Fixed Point Theorem for Weakly Inward Contractions and Fixed Point Curve in 2-Banach Space

Mathematical Journal of Interdisciplinary Sciences ◽

10.15415/mjis.2015.32015 ◽

2015 ◽

Vol 3 (2) ◽

pp. 173-182

Author(s):

P Riyas ◽

KT Ravindran

Keyword(s):

Banach Space ◽

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Unique Fixed Point ◽

Point Curve ◽

Weakly Inward

Corner contact penalty functions in plane and in space

Pollack Periodica ◽

10.1556/pollack.2.2007.2.4 ◽

2007 ◽

Vol 2 (2) ◽

pp. 39-50

Author(s):

Vanda Pomezanski

Keyword(s):

Penalty Functions