### 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. This variant

uses the square of the violation as a feasibility measure.

Original language | English |
---|---|

Publisher | Rutherford Appleton Laboratory |

Number of pages | 43 |

Volume | RAL-TR-2014-001 |

Publication status | Published - 2 Jan 2014 |

### Fingerprint

### Keywords

- Nonlinear optimization
- numerical methods
- convergence theory

### Cite this

*An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization using a Squared-Violation Feasibility Measure*. Rutherford Appleton Laboratory.

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

Research output: Working paper

TY - UNPB

T1 - An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization using a Squared-Violation Feasibility Measure

AU - Curtis, Frank

AU - Gould, N. I. M.

AU - Robinson, Daniel

AU - Toint, Ph

PY - 2014/1/2

Y1 - 2014/1/2

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. This variant uses the square of the violation as a feasibility measure.

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. This variant uses the square of the violation as a feasibility measure.

KW - Nonlinear optimization

KW - numerical methods

KW - convergence theory

M3 - Working paper

VL - RAL-TR-2014-001

BT - An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization using a Squared-Violation Feasibility Measure

PB - Rutherford Appleton Laboratory

ER -