MA57

MA57 - a code for the solution of sparse symmetric definite and indefinite systems. We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 x 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe some of the implementation details and emphasize the novel features of MA57. These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple right-hand sides, and iterative refinement and error analysis. The code is written in Fortran 77, but there are additional facilities within a Fortran 90 implementation that include the ability to identify and change pivots. Several of these facilities have been developed particularly to support optimization applications, and we illustrate the performance of the code on problems arising therefrom.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 88 articles , 1 standard article )

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  1. Kambampati, Sandilya; Chung, Hayoung; Kim, H. Alicia: A discrete adjoint based level set topology optimization method for stress constraints (2021)
  2. Agamawi, Yunus M.; Rao, Anil V.: CGPOPS: a C++ software for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation and sparse nonlinear programming (2020)
  3. Bueno, Luís Felipe; Haeser, Gabriel; Santos, Luiz-Rafael: Towards an efficient augmented Lagrangian method for convex quadratic programming (2020)
  4. Domínguez, V.; Ganesh, M.; Sayas, F. J.: An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation (2020)
  5. Duff, Iain; Hogg, Jonathan; Lopez, Florent: A new sparse (LDL^T) solver using a posteriori threshold pivoting (2020)
  6. Liao-McPherson, Dominic; Kolmanovsky, Ilya: FBstab: a proximally stabilized semismooth algorithm for convex quadratic programming (2020)
  7. Orban, Dominique; Siqueira, Abel Soares: A regularization method for constrained nonlinear least squares (2020)
  8. Zanelli, A.; Domahidi, A.; Jerez, J.; Morari, M.: FORCES NLP: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs (2020)
  9. Armand, Paul; Tran, Ngoc Nguyen: Rapid infeasibility detection in a mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization (2019)
  10. Armand, Paul; Tran, Ngoc Nguyen: An augmented Lagrangian method for equality constrained optimization with rapid infeasibility detection capabilities (2019)
  11. Birgin, E. G.; Martínez, J. M.: A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization (2019)
  12. Cui, Yiran; Morikuni, Keiichi; Tsuchiya, Takashi; Hayami, Ken: Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning (2019)
  13. Kuřátko, Jan: Factorization of saddle-point matrices in dynamical systems optimization -- reusing pivots (2019)
  14. Scott, Jennifer A.; Tůma, Miroslav: Sparse stretching for solving sparse-dense linear least-squares problems (2019)
  15. Arreckx, Sylvain; Orban, Dominique: A regularized factorization-free method for equality-constrained optimization (2018)
  16. Druinsky, Alex; Carlebach, Eyal; Toledo, Sivan: Wilkinson’s inertia-revealing factorization and its application to sparse matrices. (2018)
  17. Huber, Andreas; Gerdts, Matthias; Bertolazzi, Enrico: Structure exploitation in an interior-point method for fully discretized, state constrained optimal control problems (2018)
  18. Nicholson, Bethany L.; Wan, Wei; Kameswaran, Shivakumar; Biegler, Lorenz T.: Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems (2018)
  19. Rees, Tyrone; Scott, Jennifer: A comparative study of null-space factorizations for sparse symmetric saddle point systems. (2018)
  20. Scott, Jennifer; Tůma, Miroslav: A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows (2018)

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