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## Abstract

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.

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 |
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Publisher | Rutherford Appleton Laboratory |

Number of pages | 43 |

Volume | RAL-TR-2014-001 |

Publication status | Published - 2 Jan 2014 |

## Keywords

- Nonlinear optimization
- numerical methods
- convergence theory

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