Primal-dual interior point QP-free algorithm for nonlinear constrained optimization

作者： | Jinbao Jian, Hanjun Zeng, Guodong Ma, Zhibin Zhu |

作者单位： |
^{1}Yulin Normal University^{2}Guangxi University^{3}Guilin University of Electronic Technology |

刊名： | Journal of Inequalities and Applications, 2017, Vol.2017 (1) |

来源数据库： | Springer Journal |

DOI： | 10.1186/s13660-017-1500-2 |

关键词： | Inequality and equality constraints; Optimization; Primal-dual interior method; Working set; Global and superlinear convergence; 90C30; 49M37; 65K05; |

英文摘要： | In this paper, a class of nonlinear constrained optimization problems with both inequality and equality constraints is discussed. Based on a simple and effective penalty parameter and the idea of primal-dual interior point methods, a QP-free algorithm for solving the discussed problems is presented. At each iteration, the algorithm needs to solve two or three reduced systems of linear equations with a common coefficient matrix, where a slightly new working set technique for judging the active set is used to construct the coefficient matrix, and the positive definiteness restriction on the Lagrangian Hessian estimate is relaxed. Under reasonable conditions, the proposed algorithm is globally and superlinearly convergent. During the numerical experiments, by modifying the technique in... |

原始语种摘要： | In this paper, a class of nonlinear constrained optimization problems with both inequality and equality constraints is discussed. Based on a simple and effective penalty parameter and the idea of primal-dual interior point methods, a QP-free algorithm for solving the discussed problems is presented. At each iteration, the algorithm needs to solve two or three reduced systems of linear equations with a common coefficient matrix, where a slightly new working set technique for judging the active set is used to construct the coefficient matrix, and the positive definiteness restriction on the Lagrangian Hessian estimate is relaxed. Under reasonable conditions, the proposed algorithm is globally and superlinearly convergent. During the numerical experiments, by modifying the technique in... |