Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Idempotent structures in optimization

Tools
- Tools
+ Tools

Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2001) Idempotent structures in optimization. Journal of Mathematical Sciences, Vol.104 (No.1). pp. 847-880. doi:10.1023/A:1009514904187

[img]
Preview
PDF
WRAP_Kolokoltsov_pontr.pdf - Submitted Version - Requires a PDF viewer.

Download (404Kb)
Official URL: http://dx.doi.org/10.1023/A:1009514904187

Request Changes to record.

Abstract

Consider the set A = R ∪ {+∞} with the binary operations o1 = max
and o2 = + and denote by An the set of vectors v = (v1,...,vn) with entries
in A. Let the generalised sum u o1 v of two vectors denote the vector with
entries uj o1 vj , and the product a o2 v of an element a ∈ A and a vector
v ∈ An denote the vector with the entries a o2 vj . With these operations,
the set An provides the simplest example of an idempotent semimodule.
The study of idempotent semimodules and their morphisms is the subject
of idempotent linear algebra, which has been developing for about
40 years already as a useful tool in a number of problems of discrete optimisation.
Idempotent analysis studies infinite dimensional idempotent
semimodules and is aimed at the applications to the optimisations problems
with general (not necessarily finite) state spaces. We review here
the main facts of idempotent analysis and its major areas of applications
in optimisation theory, namely in multicriteria optimisation, in turnpike
theory and mathematical economics, in the theory of generalised solutions
of the Hamilton-Jacobi Bellman (HJB) equation, in the theory of games
and controlled Marcov processes, in financial mathematics.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Mathematical optimization, Idempotents
Journal or Publication Title: Journal of Mathematical Sciences
Publisher: Springer
ISSN: 10723374
Official Date: 2001
Dates:
DateEvent
2001Published
Volume: Vol.104
Number: No.1
Page Range: pp. 847-880
DOI: 10.1023/A:1009514904187
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us