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Optimization Problems Under Max-Min Separable Equation and Inequality Constraints

In: Decision Making and Optimization

Author

Listed:
  • Martin Gavalec

    (University of Hradec Kralove)

  • Jaroslav Ramík

    (Silesian University in Opava)

  • Karel Zimmermann

    (Charles University in Prague)

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.

Suggested Citation

  • Martin Gavalec & Jaroslav Ramík & Karel Zimmermann, 2015. "Optimization Problems Under Max-Min Separable Equation and Inequality Constraints," Lecture Notes in Economics and Mathematical Systems, in: Decision Making and Optimization, edition 127, chapter 0, pages 119-161, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-08323-0_4
    DOI: 10.1007/978-3-319-08323-0_4
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