### Abstract

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, which is designed to solve problems with both

equality and inequality constraints, achieves global convergence

guarantees by combining a trust-region methodology with a funnel

mechanism. The prominent features of our algorithm are that (i) the

subproblems that define each search direction may be solved

approximately, (ii) criticality measures for feasibility and

optimality aid in determining which subset of computations will be

performed during each iteration, (iii) no merit function or filter is

used, (iv) inexact sequential quadratic optimization steps may be

computed when advantageous, and (v) it may be implemented matrix-free

so that derivative matrices need not be formed or factorized so long

as matrix-vector products with them can be performed.

Language | English |
---|---|

Pages | 73-134 |

Number of pages | 43 |

Journal | Mathematical Programming |

Volume | 161 |

Issue number | 1 |

State | Published - Jan 2017 |

### Fingerprint

### Keywords

- Nonlinear optimization
- numerical methods
- convergence theory

### Cite this

*Mathematical Programming*,

*161*(1), 73-134.

}

*Mathematical Programming*, vol 161, no. 1, pp. 73-134.

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

Research output: Research - peer-review › 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, which is designed to solve problems with both equality and inequality constraints, achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved approximately, (ii) criticality measures for feasibility and optimality aid in determining which subset of computations will be performed during each iteration, (iii) no merit function or filter is used, (iv) inexact sequential quadratic optimization steps may be computed when advantageous, and (v) it may be implemented matrix-free so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed.

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, which is designed to solve problems with both equality and inequality constraints, achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved approximately, (ii) criticality measures for feasibility and optimality aid in determining which subset of computations will be performed during each iteration, (iii) no merit function or filter is used, (iv) inexact sequential quadratic optimization steps may be computed when advantageous, and (v) it may be implemented matrix-free so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed.

KW - Nonlinear optimization

KW - numerical methods

KW - convergence theory

M3 - Article

VL - 161

SP - 73

EP - 134

JO - Mathematical Programming

T2 - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1

ER -