Optimization problem under two-sided (max, +)/(min, +) inequality constraints

Zimmermann, Karel. "Optimization problem under two-sided (max, +)/(min, +) inequality constraints." Applications of Mathematics 65.6 (2020): 777-783. <http://eudml.org/doc/296996>.

@article{Zimmermann2020,
abstract = {$(\max ,+)$-linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form $f(x_1, \dots , x_h) = \max _j(a_j+ x_j)$, where $a_j$, $j = 1, \dots , h$, are real numbers. Similarly $(\min ,+)$-linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have $(\max ,+)$-linear functions of variables $x$ on one side and $(\min ,+)$-linear functions of variables $y$ on the other side. Such systems can be applied e.g. to operations research problems in which we need to coordinate or synchronize release and completion times of operations or departure and arrival times of passengers. A motivation example is presented and the proposed solution method is demonstrated on a small numerical example.},
author = {Zimmermann, Karel},
journal = {Applications of Mathematics},
keywords = {nonconvex optimization; $(\max ,+)/(\min ,+)$-linear functions; OR - arrival-departure coordination},
language = {eng},
number = {6},
pages = {777-783},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimization problem under two-sided (max, +)/(min, +) inequality constraints},
url = {http://eudml.org/doc/296996},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Zimmermann, Karel
TI - Optimization problem under two-sided (max, +)/(min, +) inequality constraints
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 6
SP - 777
EP - 783
AB - $(\max ,+)$-linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form $f(x_1, \dots , x_h) = \max _j(a_j+ x_j)$, where $a_j$, $j = 1, \dots , h$, are real numbers. Similarly $(\min ,+)$-linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have $(\max ,+)$-linear functions of variables $x$ on one side and $(\min ,+)$-linear functions of variables $y$ on the other side. Such systems can be applied e.g. to operations research problems in which we need to coordinate or synchronize release and completion times of operations or departure and arrival times of passengers. A motivation example is presented and the proposed solution method is demonstrated on a small numerical example.
LA - eng
KW - nonconvex optimization; $(\max ,+)/(\min ,+)$-linear functions; OR - arrival-departure coordination
UR - http://eudml.org/doc/296996
ER -