A reduction method for semi-infinite programming by means of a global stochastic approach†

^†This paper has been presented at the 8th International Conference on Parametric Optimization and Related Topics (Cairo, Egypt, November–December 2005).

Abstract

We describe a reduction algorithm for solving semi-infinite programming problems. The proposed algorithm uses the simulated annealing method equipped with a function stretching as a multi-local procedure, and a penalty technique for the finite optimization process. An exponential penalty merit function is reduced along each search direction to ensure convergence from any starting point. Our preliminary numerical results seem to show that the algorithm is very promising in practice.

^†This paper has been presented at the 8th International Conference on Parametric Optimization and Related Topics (Cairo, Egypt, November–December 2005).

Keywords:

• semi-infinite programming
• reduction method
• simulated annealing
• penalty method
• exponential function

Mathematics Subject Classifications 2000::

• 90C34
• 90C56

Acknowledgements

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

This work has been partially supported by the Algoritmi Research Center and by Portuguese FCT grant POCI/MAT/58957/2004.

Notes

^†This paper has been presented at the 8th International Conference on Parametric Optimization and Related Topics (Cairo, Egypt, November–December 2005).