Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.Expand

Numerical tests are described comparing I~QR with several other conjugate-gradient algorithms, indicating that I ~QR is the most reliable algorithm when A is ill-conditioned.Expand

An SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems is discussed.Expand

Summary. The lasso penalizes a least squares regression by the sum of the absolute values (L1-norm) of the coefficients. The form of this penalty encourages sparse solutions (with many coefficients… Expand

The method of conjugate gradients for solving systems of linear equations with a symmetric positive definite matrix A is given as a logical development of the Lanczos algorithm for tridiagonalizing...

We suggest a form for, and give a constructive derivation of, the generalized singular value decomposition of any two matrices having the same number of columns. We outline its desirable… Expand

An iterative method LSMR is presented for solving linear systems Ax = b and leastsquares problems min ‖Ax−b‖2, with A being sparse or a fast linear operator, and it is observed in practice that ‖rk‖ also decreases monotonically, so that compared to LSQR it is safer to terminate L SMR early.Expand

MINOS is a large-scale optimization system, for the solution of sparse linear and nonlinear programs, with features including a new basis package, automatic scaling of linear constraints, and automatic estimation of some or all gradients.Expand

This work was supported by Natural Sciences and Engineering Research Council of Canada Grant A8652, by the New Zealand Department of Scientific and Industrial Research, and by the Department of Energy under Contract DE-AT03-76ER72018.Expand

An algorithm for solving large-scale nonlinear programs with linear constraints is presented. The method combines efficient sparse-matrix techniques as in the revised simplex method with stable… Expand