A note on maximizing a special concave function subject to simultaneous Loewner order constraints

James Arthur Calvin*, Richard L. Dykstra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)37-44
Number of pages8
JournalLinear Algebra and Its Applications
Volume176
Issue numberC
DOIs
StatePublished - Jan 1 1992

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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