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

James A. Calvin; Richard L. Dykstra

doi:10.1016/0024-3795(92)90208-R

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

James A. Calvin^*, Richard L. Dykstra

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	37-44
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	176
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(92)90208-R
State	Published - Nov 1992
Externally published	Yes

Bibliographical note

Funding Information:
‘The majority of this work was done while the author was on the faculty of the Department of Statistics and Actuarial at the University of Iowa. This work was partially supported by National Science Foundation Grant DMS-9104673. ‘This work was partially supported by National Science Foundation Grant DMS-9003467.

ASJC Scopus subject areas

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

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10.1016/0024-3795(92)90208-R

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title = "A note on maximizing a special concave function subject to simultaneous Loewner order constraints",

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.",

author = "Calvin, {James A.} and Dykstra, {Richard L.}",

note = "Funding Information: {\textquoteleft}The majority of this work was done while the author was on the faculty of the Department of Statistics and Actuarial at the University of Iowa. This work was partially supported by National Science Foundation Grant DMS-9104673. {\textquoteleft}This work was partially supported by National Science Foundation Grant DMS-9003467.",

year = "1992",

month = nov,

doi = "10.1016/0024-3795(92)90208-R",

language = "English (US)",

volume = "176",

pages = "37--44",

journal = "Linear Algebra and Its Applications",

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AU - Calvin, James A.

AU - Dykstra, Richard L.

N1 - Funding Information: ‘The majority of this work was done while the author was on the faculty of the Department of Statistics and Actuarial at the University of Iowa. This work was partially supported by National Science Foundation Grant DMS-9104673. ‘This work was partially supported by National Science Foundation Grant DMS-9003467.

PY - 1992/11

Y1 - 1992/11

N2 - 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.

AB - 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.

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

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

Abstract

Bibliographical note

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