Interior point filter method for semi-infinite programming problems

Abstract

Semi-infinite programming (SIP) problems can be efficiently solved by reduction-type methods. Here, we present a new reduction method for SIP, where the multi-local optimization is carried out with a stretched simulated annealing algorithm, the reduced (finite) problem is approximately solved by a Newton's primal–dual interior point method that uses a novel two-dimensional filter line search strategy to guarantee the convergence to a KKT point that is a minimizer, and the global convergence of the overall reduction method is promoted through the implementation of a classical two-dimensional filter line search. Numerical experiments with a set of well-known problems are shown.

Keywords:

• nonlinear optimization
• semi-infinite programming
• interior point
• filter method
• line search

AMS Subject Classifications::

• 90C30
• 90C34
• 90C51

Acknowledgements

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