Maximization of functions with multivariate arguments can be computationally difficult. We show that for a special function, which is proportional to the density of a Wishart distribution, reparametrization can lead to maximization of a concave function. We use this fact to produce an algorithm which maximizes the function over a restricted parameter space of the form 0 < L ≤ Σ ≤ U, where L ≤ U means that U - L is a nonnegative definite matrix and L < U means that U - L is positive definite. This restriction is often referred to as the Loewner ordering.
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics