Assessing the potential of interior point barrier filter line search methods: nonmonotone versus monotone approach

Abstract

In this article, we present a numerical study of three nonmonotone filter line search techniques, as well as a three-dimensional filter approach, when incorporated into the solver IPOPT, a primal-dual barrier method developed by Wächter and Biegler [On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program. 106 (2006), pp. 25–57] for nonlinear programming. Primary assessment of the proposals has been done with sets of small- and medium-scale problems and large-scale problems separately. Results show that the use of nonmonotone globalization strategies improves efficiency.

Keywords:

• nonlinear optimization
• interior point method
• filter method
• nonmonotone line search

AMS Subject Classifications::

• 90C30
• 90C51
• 65K05

Acknowledgements

The authors thank three anonymous referees for their careful reading of the manuscript and their valuable comments and suggestions.

Notes

Notes

1. This counter gives the total number of function evaluations required by the algorithm. It counts all function evaluations in the line search procedures – in the main algorithm, in the feasibility restoration phase and in the second-order correction steps.

2. This counter gives the sum of the iterations required by all the barrier problems that are solved until a solution of the optimization problem is achieved. It counts all points that are generated and accepted by the filter until a solution with a specified tolerance is achieved.