• Publications
  • Influence
Sparse and stable Markowitz portfolios
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to theExpand
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Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints
Regularization of ill-posed linear inverse problems via ℓ1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an ℓ1Expand
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Variable Metric Inexact Line-Search-Based Methods for Nonsmooth Optimization
TLDR
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly nondifferentiable, function. Expand
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On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty
An explicit algorithm for the minimization of an l1-penalized least-squares functional, with non-separable l1 term, is proposed. Each step in the iterative algorithm requires four matrix vectorExpand
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L1Packv2: A Mathematica package for minimizing an l1-penalized functional
  • I. Loris
  • Computer Science, Mathematics
  • Comput. Phys. Commun.
  • 19 October 2007
TLDR
L1Packv2 is a Mathematica package that contains a number of algorithms that can be used for the minimization of an l 1 -penalized least squares functional. Expand
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Symmetry reductions of the BKP hierarchy
A general symmetry of the bilinear BKP hierarchy is studied in terms of tau functions. We use this symmetry to define reductions of the BKP hierarchy, among which new integrable systems can be found.Expand
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On the performance of algorithms for the minimization of l1-penalized functionals
The problem of assessing the performance of algorithms used for the minimization of an ?1-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that usesExpand
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Tomographic inversion using L1-norm regularization of wavelet coefficients
We propose the use of $ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=data$, allowing for the possibility of sharp discontinuitiesExpand
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On a direct bilinearization method : Kaup's higher-order water wave equation as a modified nonlocal Boussinesq equation
A systematic procedure for the bilinearization of classes of soliton equations is developed with the help of a generalization of Bell's exponential polynomials (1934). Application of this procedureExpand
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Iterative algorithms for total variation-like reconstructions in seismic tomography
TLDR
A qualitative comparison of total variation like penalties (total variation, Huber variant of the total variation, total generalized variation, . . .) is made in the context of global seismic tomography. Expand
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