This work proposes to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights, which regularizes (stabilizes) the optimization problem, encourages sparse portfolios, and allows accounting for transaction costs.Expand

This work proposes an alternative implementation to ℓ1-constraints, using a gradient method, with projection on ™1-balls, and proves convergence in norm for one of these projected gradient methods, without and with acceleration.Expand

A new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly nondifferentiable, function, and an Armijo-like rule to determine the stepsize ensuring the sufficient decrease of the objective function is developed.Expand

An explicit algorithm for the minimization of an l1-penalized least-squares functional, with non-separable l1 term, is proposed and a 1/N convergence rate is derived for the functional.Expand

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 uses… Expand

A general symmetry of the bilinear BKP hierarchy is studied in terms of tau functions, which are connected to constraints on the Lax operator as well as on the bil inear formulation, and a class of solutions for the reduced equations is derived.Expand

A new class of probability distributions, the so-called connected double truncated gamma distribution, is introduced. We show that using this class as the error distribution of a linear model leads… Expand

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 procedure… Expand

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 discontinuities… Expand