54 citations · 511 across the 66 of their papers we have counts for
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Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints
Nikolai Krivulin, Karel Zimmermann
We examine two multidimensional optimization problems that are formulated in terms of tropical mathematics. The problems are to minimize nonlinear objective functions, which are de…
Complete solution of a constrained tropical optimization problem with application to location analysis
Nikolai Krivulin
We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective funct…
Extremal properties of tropical eigenvalues and solutions to tropical optimization problems
Nikolai Krivulin
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 mul…
Solution of linear equations and inequalities in idempotent vector spaces
Nikolai Krivulin
Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of di…
A constrained tropical optimization problem: complete solution and application example
Nikolai Krivulin
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject…
A maximization problem in tropical mathematics: a complete solution and application examples
Nikolai Krivulin
A multidimensional optimization problem is formulated in the tropical mathematics setting as to maximize a nonlinear objective function, which is defined through a multiplicative c…