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Abstract
Tropical (idempotent) algebra, which deals with vector semimodules over idempotent semirings, finds expanding application as a promising modeling and solution tool in applied mathematics, computer science, and operations research. The progress in the area is mainly due to the fact that many complicated problems that are actually nonlinear in the ordinary sense become linear and so more tractable when translated into the language of the algebra. Among the topical lines of investigation is the development of methods and computational procedures for solution of extremal problems including idempotent analogues of linear programming problems and their extensions.
We consider multidimensional extremal problems that consist in minimization of functionals defined on semimodules over idempotent semifields. Closedform solutions to the problems are given based on methods and techniques of solving linear vector equations as well as on extremal properties of eigenvalues of irreducible matrices in idempotent algebra. We show how to apply the results to solve both unconstrained and constrained multidimensional minimax single facility location problems with rectilinear and Chebyshev distances.
We consider multidimensional extremal problems that consist in minimization of functionals defined on semimodules over idempotent semifields. Closedform solutions to the problems are given based on methods and techniques of solving linear vector equations as well as on extremal properties of eigenvalues of irreducible matrices in idempotent algebra. We show how to apply the results to solve both unconstrained and constrained multidimensional minimax single facility location problems with rectilinear and Chebyshev distances.
Original language  English 

Pages  53 
State  Published  2012 
Event  Polynomial Computer Algebra '2012  Euler International Mathematical Institute, St. Petersburg, Russian Federation Duration: 23 Apr 2012 → 28 Apr 2012 http://www.pdmi.ras.ru/EIMI/2012/pca/ 
Conference
Conference  Polynomial Computer Algebra '2012 

Abbreviated title  PCA 2012 
Country  Russian Federation 
City  St. Petersburg 
Period  23/04/12 → 28/04/12 
Internet address 
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Activities

Extremal problems in tropical mathematics: solution methods and application to location analysis
Николай Кимович Кривулин (Speaker)
23 Apr 2012Activity: Talk types › Oral presentation

Polynomial Computer Algebra '2012
Николай Кимович Кривулин (Participant)
23 Apr 2012 → 28 Apr 2012Activity: Attendance types › Participating in a conference, workshop, ...