The goal of this course is to investigate in-depth and to develop expert knowledge in the theory and algorithms for convex optimization. This course will provide a rigorous introduction to the rich ...

Mathematics of Operations Research, Vol. 31, No. 3 (Aug., 2006), pp. 433-452 (20 pages) We consider optimization problems involving convex risk functions. By employing techniques of convex analysis ...

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

where \(\mathsf{G}(\cdot)\) is some convex operator and \(\mathcal{F}\) is as set of feasible input distributions. Examples of such an optimization problem include finding capacity in information ...

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 ...