Comparing Two Interior-Point Approaches for Semi-Infinite Programs

Florian Jarre

In several attempts to generalize interior-point approaches to semi-infinite programs it has been observed that barrier methods based on the integral over some barrier function exhibit poor local convergence properties. This observation contrasts the intuition that, typically, semi-infinite programs possess a piecewise smooth boundary just like finite dimensional optimization problems for which interior-point methods have proved to be very efficient. In this paper we provide some insight in the difference of barrier methods for finitely many constraints and infinitely many constraints. We show that the integral over a barrier function can never provide a self-concordant barrier function for a semi-infinite program. We propose an alternative implicit formulation of a barrier function that shares many properties with barrier functions for finite dimensional optimization problems.

Technical Report, Institut fuer Angewandte Mathematik, Universitaet Wuerzburg, Am Hubland, March 1999.