Capra-Convexity, Convex Factorization and Variational Formulations for the ℓ0 Pseudonorm

[1]  Michael P. Friedlander,et al.  Atomic Decomposition via Polar Alignment: The Geometry of Structured Optimization , 2020, Found. Trends Optim..

[2]  J. Chancelier,et al.  Constant along primal rays conjugacies and the l 0 pseudonorm , 2020, Optimization.

[3]  J. Chancelier,et al.  Hidden Convexity in the l0 Pseudonorm , 2019, 1906.04038.

[4]  Akiko Takeda,et al.  Efficient DC Algorithm for Constrained Sparse Optimization , 2017, 1701.08498.

[5]  G. Obozinski,et al.  A unified perspective on convex structured sparsity: Hierarchical, symmetric, submodular norms and beyond , 2016 .

[6]  M. Nikolova.  Relationship between the optimal solutions of least squares regularized with L0-norm and constrained by k-sparsity , 2016 .

[7]  Massimiliano Pontil,et al.  New Perspectives on k-Support and Cluster Norms , 2014, J. Mach. Learn. Res..

[8]  Hai Yen Le,et al.  A variational approach of the rank function , 2013 .

[9]  Nathan Srebro,et al.  Sparse Prediction with the $k$-Support Norm , 2012, NIPS.

[10]  S. Gaubert,et al.  Invertibility of functional Galois connections , 2002 .

[11]  A. Rubinov.  Abstract Convexity and Global Optimization , 2000 .

[12]  E. M. Sá,et al.  Characterizations of ∗orthant-monotonic norms , 1993 .

[13]  J. Hiriart-Urruty,et al.  Convex analysis and minimization algorithms , 1993 .

[14]  Charles R. Johnson,et al.  Matrix analysis , 1985 .

[15]  R. E. Funderlic,et al.  Some characterizations of orthant monotonic norms , 1979 .

[16]  J. Stoer,et al.  Some Results on Fields of Values of a Matrix , 1967 .

[17]  David Gries,et al.  Characterizations of certain classes of norms , 1967 .

[18]  M. Friedlander,et al.  Atomic Decomposition via Polar Alignment , 2020 .

[19]  Bastian Goldlücke,et al.  Variational Analysis , 2014, Computer Vision, A Reference Guide.

[20]  Juan Enrique Martínez-Legaz,et al.  Generalized Convex Duality and its Economic Applicatons , 2005 .

[21]  R. Tyrrell Rockafellar,et al.  Variational Analysis , 1998, Grundlehren der mathematischen Wissenschaften.

[22]  I. Singer.  Abstract Convex Analysis , 1997 .

[23]  R. Tyrrell Rockafellar.  Conjugate Duality and Optimization , 1974 .

[24]  R. Rockafellar.  1. Conjugate Duality and Optimization , 1974 .

[25]  L. Mirsky.  SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS , 1960 .