Speaker: Chris Jordan-Squire
Topic: Convex Optimization on Probability Measures
Abstract:
We consider a class of convex optimization problems over the space
of regular Borel measures on a compact subset of n dimensional Euclidean space
where the measures are restricted to be probability measures.
Applications of this
class of problems are discussed including mixing density estimation,
maximum entropy, and
optimal design. We provide a complete duality theory using
perturbational techniques,
establish the equivalence of these problems to associated nonconvex
finite dimensional
problems, and then establish the equivalence between the finite and
infinite dimensional
optimality conditions. Finally, some implications for numerical
methods are discussed.