### Résumé

We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, but has the additional capability of being able to solve problems with both equality and inequality constraints. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved with matrix-free methods so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed; (ii) the subproblems may be solved approximately in all iterations; (iii) in certain situations, the computed search directions represent inexact sequential quadratic optimization steps, which may be desirable for fast local convergence; (iv) criticality measures for feasibility and optimality aid in determining whether only a subset of computations need to be performed during a given iteration; and (v) no merit function or filter is needed to ensure global convergence.

langue originale | Anglais |
---|---|

Pages (de - à) | 73-134 |

Nombre de pages | 62 |

journal | Mathematical Programming |

Volume | 161 |

Numéro de publication | 1-2 |

Les DOIs | |

état | Publié - janv. 2017 |

### Empreinte digitale

### Citer ceci

*Mathematical Programming*,

*161*(1-2), 73-134. https://doi.org/10.1007/s10107-016-1003-9

}

*Mathematical Programming*, VOL. 161, Numéro 1-2, p. 73-134. https://doi.org/10.1007/s10107-016-1003-9

**An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization.** / Curtis, Frank; Gould, N. I. M.; Robinson, Daniel; Toint, Ph.

Résultats de recherche: Contribution à un journal/une revue › Article

TY - JOUR

T1 - An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization

AU - Curtis, Frank

AU - Gould, N. I. M.

AU - Robinson, Daniel

AU - Toint, Ph

PY - 2017/1

Y1 - 2017/1

N2 - We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, but has the additional capability of being able to solve problems with both equality and inequality constraints. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved with matrix-free methods so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed; (ii) the subproblems may be solved approximately in all iterations; (iii) in certain situations, the computed search directions represent inexact sequential quadratic optimization steps, which may be desirable for fast local convergence; (iv) criticality measures for feasibility and optimality aid in determining whether only a subset of computations need to be performed during a given iteration; and (v) no merit function or filter is needed to ensure global convergence.

AB - We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, but has the additional capability of being able to solve problems with both equality and inequality constraints. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved with matrix-free methods so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed; (ii) the subproblems may be solved approximately in all iterations; (iii) in certain situations, the computed search directions represent inexact sequential quadratic optimization steps, which may be desirable for fast local convergence; (iv) criticality measures for feasibility and optimality aid in determining whether only a subset of computations need to be performed during a given iteration; and (v) no merit function or filter is needed to ensure global convergence.

KW - Nonlinear optimization

KW - numerical methods

KW - convergence theory

KW - Barrier-SQP methods

KW - Funnel mechanism

KW - Large-scale optimization

KW - Trust-region methods

KW - Constrained optimization

UR - http://www.scopus.com/inward/record.url?scp=84964049053&partnerID=8YFLogxK

U2 - 10.1007/s10107-016-1003-9

DO - 10.1007/s10107-016-1003-9

M3 - Article

VL - 161

SP - 73

EP - 134

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-2

ER -