### Abstract

We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351-369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence of negative curvature without requiring information about the inertia of the primal-dual iteration matrix. Negative curvature may arise from second-order information of the problem functions, but in fact exact second derivatives are not required in the approach. The complete algorithm is characterized by its emphasis on sufficient reductions in a model of an exact penalty function. We analyze the global behavior of the algorithm and present numerical results on a collection of test problems.

Original language | English (US) |
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Pages (from-to) | 273-299 |

Number of pages | 27 |

Journal | Mathematical Programming |

Volume | 122 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2010 |

### Keywords

- Constrained optimization
- Inexact linear system solvers
- Krylov subspace methods
- Large-scale optimization
- Nonconvex programming

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*Mathematical Programming*,

*122*(2), 273-299. https://doi.org/10.1007/s10107-008-0248-3