Applied Math And Analysis Seminar
Monday, January 30, 2012, 4:30pm, 119 Physics
Lenya Ryzhik (Stanford University)
$l_1$-minimization via a generalized Lagrange multiplier algorithm

Abstract:

We consider the basis pursuit problem: find the solution of an underdetermined system $Ax=y$ that minimizes the $l_1$-norm. We formulate a min-max principle (that, as we learned, actually goes back to 1970's) based on a Largange multiplier, and propose an iterative shrinkage-thresholding type algorithm that seems to work quite well. We show that the numerical algorithm converges to the exact solution of the basis pursuit problem. We also discuss its application to array imaging in wave propagation. The analysis is based on ODE techniques, regularization and energy methods. This is a joint work with M. Moscoso, A. Novikov and G. Papanicolaou. [video]

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