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Idempotent structures in optimization
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Kolokoltsov, V. N. (Vasiliĭ Nikitich). (2001) Idempotent structures in optimization. Journal of Mathematical Sciences, Vol.104 (No.1). pp. 847880. ISSN 10723374

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Official URL: http://dx.doi.org/10.1023/A:1009514904187
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 HamiltonJacobi 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 
Date:  2001 
Volume:  Vol.104 
Number:  No.1 
Page Range:  pp. 847880 
Identification Number:  10.1023/A:1009514904187 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
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URI:  http://wrap.warwick.ac.uk/id/eprint/39365 
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