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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.
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.
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 and a reduced-Hessian semidefinite QP solver (SQOPT) is discussed.
Sparsity and smoothness via the fused lasso
The fused lasso is proposed, a generalization that is designed for problems with features that can be ordered in some meaningful way, and is especially useful when the number of features p is much greater than N, the sample size.
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 desirable…
LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
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.
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.
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 stable…