## A Truncated SQP Algorithm for Large Scale Nonlinear Programming Problems (0)

Venue: | Advances in Optimization and Numerical Analysis: Proceedings of the Sixth Workshop on Optimization and Numerical Analysis |

Citations: | 5 - 3 self |

### BibTeX

@INPROCEEDINGS{Boggs_atruncated,

author = {Paul T. Boggs and Jon W. Tolle and Anthony J. Kearsley},

title = {A Truncated SQP Algorithm for Large Scale Nonlinear Programming Problems},

booktitle = {Advances in Optimization and Numerical Analysis: Proceedings of the Sixth Workshop on Optimization and Numerical Analysis},

year = {},

pages = {69--77},

publisher = {Kluwer Academic Publishers}

}

### OpenURL

### Abstract

We consider the inequality constrained nonlinear programming problem and an SQP algorithm for its solution. We are primarily concerned with two aspects of the general procedure, namely, the approximate solution of the quadratic program, and the need for an appropriate merit function. We first describe an (iterative) interior-point method for the quadratic programming subproblem that, no matter when it is terminated, yields a descent direction for a suggested new merit function. An algorithm based on ideas from trust-region and truncated Newton methods is suggested and some of our preliminary numerical results are discussed.

### Citations

1360 |
Practical Optimization
- Gill, Murray, et al.
- 1981
(Show Context)
Citation Context ...solved. In our testing, we use forward finite-difference approximations to gradients and Hessians, and modify the Hessian of the Lagrangian to be positive semidefinite in cases where it is not (e.g. (=-=Gill et al., 1981-=-)). This latter procedure requires the addition of a non-negative diagonal matrix to the Hessian approximation. Our observations include the following. \Gamma The number of major iterations is reasona... |

944 |
Numerical methods for unconstrained optimization and nonlinear equations
- Dennis, Schnabel
- 1983
(Show Context)
Citation Context ...one using the approximate merit function if the current iterate lies outside the j-domain. The true merit function is employed otherwise. We then use standard updating strategies to adjusts(see e.g. (=-=Dennis and Schnabel, 1983-=-) or (Mor'e and Sorensen, 1983)). Third, the penalty parameter, 8 PAUL T. BOGGS ET AL. d, is updated in a very straightforward manner. Essentially, an estimate of the condition of the problem is monit... |

235 |
Inexact Newton methods
- Dembo, Eisenstat, et al.
- 1982
(Show Context)
Citation Context ...he large scale case, solving (QP ) only approximately by an iterative interior-point algorithm that we can stop prematurely. Such ideas are in the spirit of truncated or inexact Newton methods. (See (=-=Dembo et al., 1982-=-) and, for a recent discussion of these methods, (Eisenstat and Walker, 1991).) To be more specific, we use the interior-point quadratic program solver of (Boggs et al., 1992). At each iteration this ... |

210 |
Computing a trust region step
- MoreĢ, Sorensen
- 1983
(Show Context)
Citation Context ... function if the current iterate lies outside the j-domain. The true merit function is employed otherwise. We then use standard updating strategies to adjusts(see e.g. (Dennis and Schnabel, 1983) or (=-=Mor'e and Sorensen, 1983-=-)). Third, the penalty parameter, 8 PAUL T. BOGGS ET AL. d, is updated in a very straightforward manner. Essentially, an estimate of the condition of the problem is monitored. In the event that this e... |

13 |
A strategy for global convergence in a sequential quadratic programming algorithm
- Boggs, Tolle
- 1989
(Show Context)
Citation Context ...unction is a scalar valued function with a minimum at the solution to (NLP ). Thus reducing this function ensures progress and allows for the construction of a globally convergent scheme. (See e.g., (=-=Boggs and Tolle, 1989-=-) and (Boggs et al., 1991).) In a previous paper, (Boggs et al., 1991), the authors introduced a merit function for (NLP ) and showed that it is appropriate for use with the SQP algorithm. In this pap... |

8 |
An interior-point method for linear and quadratic programming problems
- Boggs, Domich, et al.
- 1994
(Show Context)
Citation Context ...unction with a minimum at the solution to (NLP ). Thus reducing this function ensures progress and allows for the construction of a globally convergent scheme. (See e.g., (Boggs and Tolle, 1989) and (=-=Boggs et al., 1991-=-).) In a previous paper, (Boggs et al., 1991), the authors introduced a merit function for (NLP ) and showed that it is appropriate for use with the SQP algorithm. In this paper we apply these ideas t... |

8 |
Optimizing over three-dimensional subspaces in an interior-point method for linear programming", Linear Algebra and Its
- Domich, Boggs, et al.
- 1991
(Show Context)
Citation Context ...extended to QP with both good numerical results and particularly interesting properties with respect to the SQP method is the optimal subspace method of Boggs, et al. (Boggs et al., 1992). (See also (=-=Domich et al., 1991-=-).) We take the QP of x1 to be of the form min ffi c T ffi + 1 2 ffi T Qffi subject to: A T ffi + bs0 (1) where c; ffi 2 ! n , Q 2 ! n\Thetan , A 2 ! n\Thetam , and b 2 ! m . The assumptions on (1) th... |

7 | A family of descent functions for constrained optimization - Boggs, Tolle - 1984 |

5 | A merit function for inequality constrained nonlinear programming problems
- Boggs, Tolle, et al.
- 1991
(Show Context)
Citation Context ...unction with a minimum at the solution to (NLP ). Thus reducing this function ensures progress and allows for the construction of a globally convergent scheme. (See e.g., (Boggs and Tolle, 1989) and (=-=Boggs et al., 1991-=-).) In a previous paper, (Boggs et al., 1991), the authors introduced a merit function for (NLP ) and showed that it is appropriate for use with the SQP algorithm. In this paper we apply these ideas t... |

4 | Large Scale Numerical Optimization: Introduction and overview - Coleman - 1992 |

1 | Large-scale nonlinear constrained optimization - unknown authors - 1992 |