Optimization Problems Under Max-Min Separable Equation and Inequality Constraints

Martin Gavalec, Jaroslav Ramík and Karel Zimmermann
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Martin Gavalec: University of Hradec Kralove
Jaroslav Ramík: Silesian University in Opava
Karel Zimmermann: Charles University in Prague

Chapter Chapter 4 in Decision Making and Optimization, 2015, pp 119-161 from Springer

Abstract: Abstract Equation and inequality systems, in which functions of the form $$\displaystyle{\max _{j\in J}(\min (a_{j},r_{j}(x_{j})))}$$ occur are studied (J is a finite index set, a j are real numbers, $$r_{j}(x_{j})$$ are strictly increasing functions). The functions occur either on one side of the relations or on both sides of them. In the former case we call the relations one-sided, in the latter case two-sided. Properties of equation and inequality systems with max, min-separable functions on one or both sides of the relations, as well as optimization problems under (max, min)-separable equation and inequality constraints are studied. For the optimization problems with one-sided (max, min)-separable constraints an explicit solution formula is derived, a duality theory is developed and some optimization problems on the set of points attainable by the functions occurring in the constraints are solved. Solution methods for some classes of optimization problems with two-sided equation and inequality constraints are proposed in the last part of this chapter.

Keywords: Inequality System; Explicit Solution Formula; Small Numerical Example; Dual Minimization Problem; Reformulated Optimization Problem (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-319-08323-0_4

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DOI: 10.1007/978-3-319-08323-0_4

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