Exact Regularization of Convex Programs

2008 ◽  
Vol 18 (4) ◽  
pp. 1326-1350 ◽  
Author(s):  
Michael P. Friedlander ◽  
Paul Tseng
Keyword(s):  
Convex Programs ◽  
Exact Regularization

Further Development in the Global Resolution of Convex Programs with Complementarity Constraints

2014 ◽  
Author(s):  
John E. Mitchell ◽  
Jong-Shi Pang ◽  
Yu-Ching Lee ◽  
Bin Yu ◽  
Lijie Bai
Keyword(s):  
Complementarity Constraints ◽  
Convex Programs ◽  
Further Development

Exact Regularization of Polyhedral Norms

2012 ◽  
Vol 22 (4) ◽  
pp. 1206-1223 ◽  
Author(s):  
Frank Schöpfer
Keyword(s):  
Polyhedral Norms ◽  
Exact Regularization

scholarly journals Critical point approximation through exact regularization

1988 ◽  
Vol 50 (181) ◽  
pp. 139-139
Author(s):  
Enrique Fern{ández Cara ◽  
Carlos Moreno
Keyword(s):  
Critical Point ◽  
Point Approximation ◽  
Exact Regularization

scholarly journals Exact solutions of infinite dimensional total-variation regularized problems

2018 ◽  
Vol 8 (3) ◽  
pp. 407-443 ◽  
Author(s):  
Axel Flinth ◽  
Pierre Weiss
Keyword(s):  
Inverse Problems ◽  
Exact Solutions ◽  
Total Variation ◽  
Linear Mapping ◽  
Scattered Data Approximation ◽  
Convex Programs ◽  
Linear Measurements ◽  
Data Approximation ◽  
Infinite Dimensional ◽  
Finite Dimensional

Abstract We study the solutions of infinite dimensional inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary function. The first contribution describes the solution’s structure: we show that under mild assumptions, there always exists an $m$-sparse solution, where $m$ is the number of linear measurements of the signal. Our second contribution is about the computation of the solution. While most existing works first discretize the problem, we show that exact solutions of the infinite dimensional problem can be obtained by solving one or two consecutive finite dimensional convex programs depending on the measurement functions structures. We finish by showing an application on scattered data approximation. These results extend recent advances in the understanding of total-variation regularized inverse problems.

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