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Generalized Variance of Multivariate Omega Functions and Duality

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  • Lee Papayanopoulos

Abstract

The covariance of probabilistic variables and the geometry of cones in deterministic optimization traditionally belong in distinct domains of study. This paper aims to show a relationship between the generalized variance of multidimensional joint omega functions and the duality of certain linear programs. Omega distributions are ubiquitous, polymorphic, and multifunctional but have been overlooked, partly due to a lack of closed form. However, the covariance/correlation matrix of joint omega functions can be stated. The geometry that links distributional covariance and generalized variance to the volume of dual cones is an exquisitely simple one. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Lee Papayanopoulos, 2002. "Generalized Variance of Multivariate Omega Functions and Duality," Annals of Operations Research, Springer, vol. 116(1), pages 21-40, October.
    • Handle: RePEc:spr:annopr:v:116:y:2002:i:1:p:21-40:10.1023/a:1021307725419
    DOI: 10.1023/A:1021307725419
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