Citation
Ys. Kan et Ai. Kibzun, CONVEXITY PROPERTIES OF PROBABILITY AND QUANTILE FUNCTIONS IN OPTIMIZATION PROBLEMS, Automation and remote control, 57(3), 1996, pp. 368-383
Citations number
30
Categorie Soggetti
Controlo Theory & Cybernetics","Computer Application, Chemistry & Engineering","Instument & Instrumentation","Robotics & Automatic Control
Journal title
ISSN journal
00051179
Volume
57
Issue
3
Year of publication
1996
Part
1
Pages
368 - 383
Database
ISI
SICI code
0005-1179(1996)57:3<368:CPOPAQ>2.0.ZU;2-3
Abstract
A survey is given of investigations on the convexity properties of pro
bability cord quantile functions in models of stochastic programming a
nd optimal control. Some conceptual contradictions of various approach
es to the problem of the probability function convexity are treated. T
he notions of partially g-concave functions and: probability measures
g-concave relative to a convex set are introduced to obviate these con
tradictions. A theorem on the convexity and g-convexity of a quantile
function is proved.