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 60 articles , 1 standard article )

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  1. Steffen, Kyle R.; Epshteyn, Yekaterina; Zhu, Jingyi; Bowler, Megan J.; Deming, Jody W.; Golden, Kenneth M.: Network modeling of fluid transport through sea ice with entrained exopolymeric substances (2018)
  2. Armand, Paul; Omheni, Riadh: A mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization (2017)
  3. Carson, Erin; Higham, Nicholas J.: A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems (2017)
  4. Gould, Nicholas I.M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
  5. Gould, Nicholas; Scott, Jennifer: The state-of-the-art of preconditioners for sparse linear least-squares problems (2017)
  6. Huang, Kuo-Ling; Mehrotra, Sanjay: Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method (2017)
  7. Koehler, Sarah; Danielson, Claus; Borrelli, Francesco: A primal-dual active-set method for distributed model predictive control (2017)
  8. Pecci, Filippo; Abraham, Edo; Stoianov, Ivan: Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks (2017)
  9. Scott, Jennifer: On using Cholesky-based factorizations and regularization for solving rank-deficient sparse linear least-squares problems (2017)
  10. Suñagua, Porfirio; Oliveira, Aurelio R.L.: A new approach for finding a basis for the splitting preconditioner for linear systems from interior point methods (2017)
  11. Wan, Wei; Biegler, Lorenz T.: Structured regularization for barrier NLP solvers (2017)
  12. Cannataro, Begüm Şenses; Rao, Anil V.; Davis, Timothy A.: State-defect constraint pairing graph coarsening method for Karush-Kuhn-Tucker matrices arising in orthogonal collocation methods for optimal control (2016)
  13. Chiang, Nai-Yuan; Zavala, Victor M.: An inertia-free filter line-search algorithm for large-scale nonlinear programming (2016)
  14. Forsgren, Anders; Gill, Philip E.; Wong, Elizabeth: Primal and dual active-set methods for convex quadratic programming (2016)
  15. Hager, William W.; Zhang, Hongchao: Projection onto a polyhedron that exploits sparsity (2016)
  16. Janka, Dennis; Kirches, Christian; Sager, Sebastian; Wächter, Andreas: An SR1/BFGS SQP algorithm for nonconvex nonlinear programs with block-diagonal Hessian matrix (2016)
  17. Gill, Philip E.; Wong, Elizabeth: Methods for convex and general quadratic programming (2015)
  18. Janka, Dennis: Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential-algebraic equations (2015)
  19. Armand, Paul; Benoist, Joël; Omheni, Riadh; Pateloup, Vincent: Study of a primal-dual algorithm for equality constrained minimization (2014)
  20. Gerdts, Matthias; Kunkel, Martin: Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation (2014)

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