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.
Contact: [email protected]