Publication: Sensitivity of Pareto Solutions in Multiobjective Optimization
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2005-08
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Springer
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Abstract
The paper presents a sensitivity analysis of Pareto solutions
on the basis of the Karush-Kuhn-Tucker (KKT) necessary conditions
applied to nonlinear multiobjective programs (MOP) continuously
depending on a parameter. Since the KKT conditions are of the first
order, the sensitivity properties are considered in the first approximation.
An analogue of the shadow prices, well known for scalar linear
programs, is obtained for nonlinear MOPs. Two types of sensitivity
are investigated: sensitivity in the state space (on the Pareto set) and
sensitivity in the cost function space (on the balance set) for a vector
cost function. The results obtained can be used in applications for
sensitivity computation under small variations of parameters. Illustrative
examples are presented.
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Keywords
Sensitivity analysis, Nonscalarized multiobjective programming, Pareto set, Balance set
Bibliographic citation
Journal of Optimization Theory and Applications, 2005, v. 126, nº 2, pp. 247-264