FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 6, PAGES 3-21

Optimization problems under $(max,min)$-linear equation and/or inequality constraints

M. Gavalec
M. Gad
K. Zimmermann

Abstract

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The paper is a survey of recent results concerning optimization problems whose set of feasible solutions is described by a finite system of so-called $(max,min)$-linear equations and/or inequalities. The objective function is equal to the maximum of a finite number of continuous unimodal functions $f$_j: R ® R each depending on one variable $x$_j Î R = (-¥, +¥). Motivation problems from the area of operations research, illustrative numerical examples, and hints for further research are included.

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Last modified: November 21, 2012