Sensitivity of Pareto Solutions in Multiobjective Optimization
AbstractThe 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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Bibliographic InfoPaper provided by Universidad Carlos III de Madrid in its series Open Access publications from Universidad Carlos III de Madrid with number info:hdl:10016/13056.
Length: 266 p.
Date of creation: Aug 2005
Date of revision:
Publication status: Published in Journal of Optimization Theory and Applications (2005-08) v.v. 126, p.247-264
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Web page: http://www.uc3m.es
Sensitivity analysis; Nonscalarized multiobjective programming; Pareto set; Balance set;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Balbás, Alejandro & Jiménez Guerra, Pedro, 1996. "Sensitivity Analysis for Convex Multiobjective Programming in Abstract Spaces," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/6344, Universidad Carlos III de Madrid.
- Balbás, Alejandro & Mayoral, Silvia, 2006. "Nonconvex optimization for pricing and hedging in imperfect markets," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/13024, Universidad Carlos III de Madrid.
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