Tropical optimization problems: recent results and applications examples

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Abstract

We consider multidimensional optimization problems formulated in the tropical mathematics setting to minimize or maximize functions defined on vectors over idempotent semifields, subject to linear equality and inequality constraints. We start with a brief overview of known tropical optimization problems and solution approaches. Furthermore, some new problems are presented with nonlinear objective functions calculated using multiplicative conjugate transposition of vectors, including problems of Chebyshev approximation, problems of approximation in the Hilbert seminorm, and pseudo-quadratic problems. To solve these problems, we apply methods based on the reduction to the solution of parametrized inequalities, matrix sparsification, and other techniques. The methods offer direct solutions represented in a compact explicit vector form ready for further analysis and straightforward computation. We conclude with a short discussion of the application of the results obtained to practical problems in location analysis, project scheduling and decision making.
Original languageEnglish
Pages38-38
Publication statusPublished - Aug 2018
EventModeling and Optimization: Theory and Applications - Lehigh University, Bethlehem
Duration: 15 Aug 201817 Aug 2018
http://coral.ie.lehigh.edu/~mopta/

Conference

ConferenceModeling and Optimization: Theory and Applications
Abbreviated titleMOPTA 2018
CountryUnited States
CityBethlehem
Period15/08/1817/08/18
Internet address

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Optimization Problem
Semifield
Project Scheduling
Chebyshev Approximation
Seminorm
Transposition
Approximation Problem
Equality Constraints
Linear Constraints
Inequality Constraints
Direct Method
Nonlinear Function
Idempotent
Hilbert
Matrix Inequality
Multiplicative
Objective function
Decision Making
Maximise
Optimization problem

Scopus subject areas

  • Control and Optimization
  • Algebra and Number Theory
  • Management Science and Operations Research

Cite this

Кривулин, Н. К. (2018). Tropical optimization problems: recent results and applications examples. 38-38. Abstract from Modeling and Optimization: Theory and Applications, Bethlehem, .
Кривулин, Николай Кимович. / Tropical optimization problems: recent results and applications examples. Abstract from Modeling and Optimization: Theory and Applications, Bethlehem, .
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Tropical optimization problems: recent results and applications examples. / Кривулин, Николай Кимович.

2018. 38-38 Abstract from Modeling and Optimization: Theory and Applications, Bethlehem, .

Research output

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Кривулин НК. Tropical optimization problems: recent results and applications examples. 2018. Abstract from Modeling and Optimization: Theory and Applications, Bethlehem, .