Skip to Main content Skip to Navigation
Reports

Theory of Cost Measures : Convergence of Decision Variables

Abstract : Considering probability theory in which the semifield of positive real numbers is replaced by the idempotent semifield of real numbers (union infinity) endowed with the min and plus laws leads to a new formalism for optimization. Probability measures correspond to minimums of functions that we call cost measures, whereas random variables correspond to constraints on these optimization problems that we call decision variables. We review in this context basic notions of probability theory -- random variables, convergence of random variables, characteristic functions,, $L^p$ norms. Whenever it is possible, results and definitions are stated in a general idempotent semiring
Document type :
Reports
Complete list of metadata

Cited literature [26 references]  Display  Hide  Download

https://hal.inria.fr/inria-00074074
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 2:26:31 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:11:33 PM

Identifiers

  • HAL Id : inria-00074074, version 1

Collections

Citation

Marianne Akian. Theory of Cost Measures : Convergence of Decision Variables. [Research Report] RR-2611, INRIA. 1995. ⟨inria-00074074⟩

Share

Metrics

Record views

241

Files downloads

1561