TY - CONF

T1 - Tropical optimization problems: recent results and applications examples

AU - Кривулин, Николай Кимович

N1 - Krivulin N. Tropical optimization problems: recent results and applications examples. In DIMACS/TRIPODS/MOPTA, 13-17 August ’18, Lehigh University, Bethlehem, PA, USA. Program and Abstracts. P.38. URL:https://coral.ise.lehigh.edu/~mopta/dimacs_tripods_mopta_2018.pdf

PY - 2018/8

Y1 - 2018/8

N2 - 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.

AB - 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.

UR - https://coral.ise.lehigh.edu/~mopta/dimacs_tripods_mopta_2018.pdf

M3 - Abstract

SP - 38

T2 - Modeling and Optimization: Theory and Applications

Y2 - 15 August 2018 through 17 August 2018

ER -