Sensitivity of Pareto Solutions in Multiobjective Optimization

A. Balbás, E. Galperin and P. Jiménez. Guerra
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A. Balbás: Universidad Carlos III
E. Galperin: Université du Québec à Montréal
P. Jiménez. Guerra: Universidad Nacional de Educación a Distancia

Journal of Optimization Theory and Applications, 2005, vol. 126, issue 2, No 2, 247-264

Abstract: 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.

Keywords: Sensitivity analysis; nonscalarized multiobjective programming; Pareto set; balance set (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-005-4713-3

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