## Nonlinear programming without a penalty function (2002)

Venue: | Mathematical Programming |

Citations: | 2 - 1 self |

### BibTeX

@ARTICLE{Gould02nonlinearprogramming,

author = {Nicholas I. M. Gould},

title = {Nonlinear programming without a penalty function},

journal = {Mathematical Programming},

year = {2002},

volume = {91},

pages = {239--269}

}

### OpenURL

### Abstract

a filter

### Citations

180 | Nonlinear programming without a penalty function - Fletcher, Leyffer - 2002 |

139 |
The conjugate gradient methods and trust regions in large scale optimization
- Steihaug
- 1983
(Show Context)
Citation Context ...ormal step are very reasonable in practice, as it is known that they hold if, for instance, nk is computed by applying one or more steps of a truncated conjugate-gradient method (see Toint, 1981, and =-=Steihaug, 1983-=-) to the minimization of the square of the linearized infeasibility. Note that the conditions (2.3), (2.4) and (2.5) allow us to choose a null normal step (nk = 0) if xk is feasible. Having computed t... |

131 | CUTE: constrained and unconstrained testing environment - Toint - 1995 |

112 | A trust region method based on interior point techniques for nonlinear programming - Byrd, Gilbert, et al. |

109 | Applied nonlinear programming - Himmelblau - 1972 |

77 | An interior point algorithm for large scale nonlinear programming - Byrd, Hribar, et al. |

42 | On the implementation of an algorithm for large-scale equality constrained optimization - Lalee, Nocedal, et al. - 1998 |

40 | Trust region algorithms for optimization with nonlinear equality and inequality constraints - Omojokun - 1989 |

38 | A reduced Hessian method for large-scale constrained optimization - Biegler, Nocedal, et al. - 1995 |

38 | An algorithm for nonlinear optimization using linear programming and equality constrained subproblems - Byrd, Gould, et al. - 2004 |

33 | Solving the trust-region subproblem using the Lanczos method - Toint - 1999 |

24 |
A superlinearly convergent algorithm for constrained optimization problems
- Mayne, Polak
- 1982
(Show Context)
Citation Context ... preliminary numerical experience discussed in the next section has shown that our algorithm, like many SQP methods, might suffer from the Maratos effect. A well documented cure for this problem (see =-=Mayne and Polak, 1982-=-, Coleman and Conn, 1982, or Section 15.3.2 of Conn et al., 2000) is to use second-order correction steps. In our context, we define a such a step sC k as a step performed from xk + sk to correct for ... |

22 | On the solution of equality constrained quadratic problems arising in optimization - Gould, Hribar, et al. |

21 |
Nonlinear programming via an exact penalty function: asymptotic analysis
- COLEMAN, CONN
- 1982
(Show Context)
Citation Context ...experience discussed in the next section has shown that our algorithm, like many SQP methods, might suffer from the Maratos effect. A well documented cure for this problem (see Mayne and Polak, 1982, =-=Coleman and Conn, 1982-=-, or Section 15.3.2 of Conn et al., 2000) is to use second-order correction steps. In our context, we define a such a step sC k as a step performed from xk + sk to correct for an unsuccessful f-iterat... |

21 | Analysis of inexact trust-region SQP algorithms - Heinkenschloss, Vicente |

18 | Global convergence of trust-region SQP-filter algorithms for general nonlinear programming - Toint, Wächter - 2002 |

9 | Sparse matrices and their uses - DUFF, ed - 1981 |

6 | A robust trust region algorithm for solving general nonlinear programming - Liu, Yuan |

5 | Global convergence without the assumption of linear independence for a trust-region algorithm for constrained optimization - El-Alem - 1995 |

5 | A multidimensional filter algorithm for nonlinear equations and nonlinear least squares - Toint |

4 | Dynamical control of infeasibility in nonlinearly constrained optimization. Presentation at the Optimization 98 Conference - Bielschowsky, Gomes - 1998 |

3 | Finding a point in the relative interior of a polyhedron - Cartis, Gould - 2007 |

3 | A global convergence theory for a general class of trust-region-based algorithms for constrained optimization without assuming regularity - El-Alem - 1996 |

2 |
Trust-Region Methods. Number 01
- Toint
- 2000
(Show Context)
Citation Context ... (1995), El-Alem (1995, 1999), Byrd, Gilbert and Nocedal (2000a), Byrd, Hribar and Nocedal (2000b), Liu and Yuan (2000) and Lalee, Nocedal and Plantenga (1998) (also see Chapter 15 of Conn, Gould and =-=Toint, 2000-=-). The algorithm presented here has four main features. The first is that it attempts to consider the objective function and the constraints as independently as possible by using different models and ... |