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

Abstract

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 R = (−∞,+). Motivation problems from the area of operations research, illustrative numerical examples, and hints for further research are included.

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Correspondence to Martin Gavalec.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 6, pp. 3–21, 2011/12.

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Gavalec, M., Gad, M. & Zimmermann, K. Optimization problems under (max, min)-linear equations and/or inequality constraints. J Math Sci 193, 645–658 (2013). https://doi.org/10.1007/s10958-013-1492-5

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Keywords

  • Feasible Solution
  • Preceding Section
  • Inequality Constraint
  • Maximal Element
  • Linear Inequality