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Abstract
An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular cases, the minimum in the problem is known to be equal to the tropical spectral radius of the matrix. We examine the problem in the common setting of a general idempotent semifield. A complete direct solution in a compact vector form is obtained to this problem under fairly general conditions. The result is extended to solve new tropical optimization problems with more general objective functions and inequality constraints. Applications to realworld problems that arise in project scheduling are presented. To illustrate the results obtained, numerical examples are also provided.
Original language  English 

Pages (fromto)  211232 
Journal  Linear Algebra and Its Applications 
Volume  468 
Early online date  8 Jul 2014 
DOIs  
State  Published  2015 
Scopus subject areas
 Control and Optimization
 Algebra and Number Theory
Keywords
 Idempotent semifield
 Eigenvalue
 Linear inequality
 Optimization problem
 Direct solution
 Project scheduling
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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