This course discusses basic convex analysis (convex sets, functions, and optimization problems), optimization theory (linear, quadratic, semidefinite, and geometric programming; optimality conditions ...

Let Γ(X) denote the proper, lower semicontinuous, convex functions on a Banach space X, equipped with the completely metrizable topology of uniform convergence of distance functions on bounded sets.

Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown ...