Activities per year
Abstract
We consider linear operators on finitedimensional semimodules over idempotent semifields (tropical linear operators) and examine extremal properties of their spectrum. It turns out that the minimum value for some nonlinear functionals that involve tropical linear operators and use multiplicative conjugate transposition is determined by their maximum eigenvalue, where the minimum and maximum are thought in the sense of the order induced by the idempotent addition in the carrier semifield. We exploit the extremal properties to solve multidimensional optimization problems formulated in the tropical mathematics setting as to minimize the functionals under constraints in the form of linear equations and inequalities. Complete closedform solutions are given by using a compact vector representation. Applications of the results to realworld problems are presented, including solutions to both unconstrained and constrained multidimensional minimax single facility location problems with rectilinear and Chebyshev distances.
Original language  English 

Pages  40 
State  Published  2013 
Event  18th Conference of the International Linear Algebra Society  Providence, United States Duration: 3 Jun 2013 → 7 Jun 2013 Conference number: 18 http://www.ilas2013.com/ 
Conference
Conference  18th Conference of the International Linear Algebra Society 

Abbreviated title  ILAS 2013 
Country  United States 
City  Providence 
Period  3/06/13 → 7/06/13 
Internet address 
Scopus subject areas
 Algebra and Number Theory
 Control and Optimization
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Activities

18th Conference of the International Linear Algebra Society
Николай Кимович Кривулин (Participant)
3 Jun 2013 → 7 Jun 2013Activity: Attendance types › Participating in a conference, workshop, ...

Extremal properties of tropical eigenvalues and solutions of tropical optimization problems
Николай Кимович Кривулин (Speaker)
4 Jun 2013Activity: Talk types › Oral presentation