On the min-max graph in finite and semi-infinite optimization
Hubertus Th. Jongen
RWTH Aachen University (D) and University Maastricht (NL)
We consider finite dimensional smooth optimization problems with compact
connected feasible set. A variable (= Riemannian) metric defines an ascent and
descent semi-flow. This
gives rise to a bipartite digraph on the set of local
minimizers and
maximizers (min-max graph). Active
set strategy may cause a
stable obstruction to the connectedness of the min-max graph. However,
by means
of an automatic constraint-adaptation of the metric the min-max graph
becomes
generically connected. In case of a single smooth inequality constraint
We give an explicit formula of the metric adaptation. In case of
finitely many
constraints we propose a logarithmic pre-smoothing and for semi-infinite
optimization we discuss a mollifier-pre-smoothing.
This is joint work with Oliver Stein.
References:
1. Jongen, H.Th., Stein, O.: Constrained global optimization:
adaptive gradient
flows. In: Frontiers in
Global Optimization (Eds.: C.A. Floudas, P. Pardalos),
Kluwer
Academic Publishers, Boston, pp. 223-236 (2004).
|
2.
Floudas, C.A.,
Jongen, H.Th.: Global
optimization: local minima and transition points.
Journal of Global Optimization, pp. 409-415 (2005)
|