User guide for QPOPT: Fortran package for constrained linear least-squares and convex quadratic programming. QPOPT is a set of Fortran 77 subroutines for minimizing a general quadratic function subject to linear constraints and simple upper and lower bounds. QPOPT may also be used for linear programming and for finding a feasible point for a set of linear equalities and inequalities. If the quadratic function is convex (i.e., the Hessian is positive definite or positive semidefinite), the solution obtained will be a global minimizer. If the quadratic is non-convex (i.e., the Hessian is indefinite), the solution obtained will be a local minimizer or a dead-point. A two-phase active-set method is used. The first phase minimizes the sum of infeasibilities. The second phase minimizes the quadratic function within the feasible region, using a reduced Hessian to obtain search directions. The method is most efficient when many constraints or bounds are active at the solution. QPOPT is not intended for large sparse problems, but there is no fixed limit on problem size.

References in zbMATH (referenced in 17 articles )

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  1. Wang, Guoqiang; Yu, Bo: PAL-Hom method for QP and an application to LP (2019)
  2. Weber, Tobias; Sager, Sebastian; Gleixner, Ambros: Solving quadratic programs to high precision using scaled iterative refinement (2019)
  3. Kouzoupis, Dimitris; Frison, Gianluca; Zanelli, Andrea; Diehl, Moritz: Recent advances in quadratic programming algorithms for nonlinear model predictive control (2018)
  4. Gould, Nicholas I. M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
  5. Verschueren, Robin; Zanon, Mario; Quirynen, Rien; Diehl, Moritz: A sparsity preserving convexification procedure for indefinite quadratic programs arising in direct optimal control (2017)
  6. Forsgren, Anders; Gill, Philip E.; Wong, Elizabeth: Primal and dual active-set methods for convex quadratic programming (2016)
  7. Mommer, Mario S.; Sommer, Andreas; Schlöder, Johannes P.; Bock, H. Georg: A nonlinear preconditioner for optimum experimental design problems (2015)
  8. Kirches, Christian: Fast numerical methods for mixed-integer nonlinear model-predictive control (2011)
  9. Kirches, Christian; Bock, Hans Georg; Schlöder, Johannes P.; Sager, Sebastian: A factorization with update procedures for a KKT matrix arising in direct optimal control (2011)
  10. Kirches, Christian; Bock, Hans Georg; Schlöder, Johannes P.; Sager, Sebastian: Block-structured quadratic programming for the direct multiple shooting method for optimal control (2011)
  11. Gould, Nicholas I. M.; Robinson, Daniel P.: A second derivative SQP method: global convergence (2010)
  12. Potschka, Andreas; Bock, Hans Georg; Schlöder, Johannes P.: A minima tracking variant of semi-infinite programming for the treatment of path constraints within direct solution of optimal control problems (2009)
  13. Bartlett, Roscoe A.; Biegler, Lorenz T.: QPSchur: A dual, active-set, Schur-complement method for large-scale and structured convex quadratic programming (2006)
  14. Oh, Seyoung; Yun, Jae Heon; Chung, Sei-Young: A quadratic approximation for protein sequence to structure mapping. (2003)
  15. Lawrence, Craig T.; Tits, André L.: A computationally efficient feasible sequential quadratic programming algorithm (2001)
  16. Park, Hyungju; Michelena, Nestor; Kulkarni, Devadatta; Papalambros, Panos: Convergence criteria for hierarchical overlapping coordination of linearly constrained convex design problems (2001)
  17. Gabriel, S. A.: An NE/SQP method for the bounded nonlinear complementarity problem (1998)