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Atomic Decomposition by Basis Pursuit
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
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
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
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
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
Sparsity and smoothness via the fused lasso
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 coefficientsExpand
Solution of Sparse Indefinite Systems of Linear Equations
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...
Towards a Generalized Singular Value Decomposition
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 desirableExpand
LSMR: An iterative algorithm for sparse least-squares problems
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 5. 0 user's guide
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
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
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
Large-scale linearly constrained optimization
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 stableExpand