Global convergence of a semi-infinite optimization method
algorithm for minimizing locally Lipschitz functions
using approximate function values is presented.
It yields a method for
minimizing semi-infinite exact penalty functions
that parallels the trust region methods used in composite nondifferentiable
A finite method for approximating
a semi-infinite exact penalty function is developed.
A uniform implicit function theorem is established
during this development.
An implementation and test results for
the approximate penalty function are included.