The weighted sum approach for finding Pareto optimal solutions in multiobjective optimization has been presented depending on a parameter value. We show that the one-parametric optimization techniques can be applied to parametric multiobjective optimization.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bank, B., Guddat, J., Klatte, D., Kummer, B., Tammer, K.: Nonlinear Parametric Optimization. Akademie-Verlag, Berlin (1990)
Dentcheva, D., Guddat, J., Rückmann, J.-J., Wendler, K.: Pathfollowing Methods in Nonlinear Optimization III: Lagrange Multiplier Embedding. Mathematical Methods of Operations Research, 41, 1432–2994 (1995)
Choo, E.V., Atkins, D.R.: Proper Efficiency in Nonconvex Multicriprogramming. Mathematics of Operations Research 8, 467–470 (1983)
Ergroff, M.: Multicriteria Optimization. Lecture Notes in Economics and Mathematical Systems, Springer 491, Berlin (2000)
Enkhbat, R., Guddat, J.: From Linear Parametric Optimization to Nonlinear Parametric Optimization: Methods and Algorithms, Survey. Journal of Mongolian Mathematical Society, 7, 35–50 (2003)
Gass, S.I.: Linear Programming. Fizmatgiz, Moscow (1961)
Gearhard, W.B.: On Vectorial Approximation. Journal of Approximation Theory, 10, 49–63 (1974)
Gol’shtein, E.G., Yudin, D.B.: New Directions in Linear Programming. Soviet Radio, Moscow (1966)
Guddat, J., Guerra, F., Jongen, H.Th.: Parametric Optimization: Singularities Pathfollowing and Jumps. E.G. Teubner. John Wiley, Chichester (1990)
Guddat, J., Guerra, F., Nowack, D.: On the Role of the Mangasarian-Fromovitz Constraints Qualification for Penalty, Exast Penalty and Lagrange Multiplier Methods. In: Fiacco, A.V. (Ed.) Mathematical Programming with Data Perturbations, Marcel Dekker, New York, 159–183 (1997)
Guddat, J., Ruckmann, J.: One-Parametric Optimization: Jumps in the Set of Generalized Critical Points. Control and Cybernetics, 23(1/2), 139–151 (1994)
Guddat, J., Jongen, H.Th., Kummer, B., Nozicka, F.: Parametric Optimization and Related Topics III. Peter Lang Verlag, Frankfurt A.M. (1993)
Jahn, J.: Vector Optimization: Theory, Applications and Extensions. Springer, New York, (2004)
Jahn, J.: Scalarization in Vector Optimization. Mathematical Programming, 29, 203–218 (1984)
Luc, D.T.: Theory of Vector Optimization. Springer, Berlin (1989)
Jongen, H.Th., Jonker, P., Twilt, F.: Critical Sets in Parametric Optimization. Mathematical Programming, 34, 333–353 (1986)
Nakayama, H.: Trade-off Analysis using Parametric Optimization Techniques, Europian Journal of Operational Research, 60, 87–98 (1992)
Nozicka, F., Guddat, J., Hollatz, H., Bank, B.: Theorie Der Linearen Parametrischen Optimierung. Akademie-Verlag, Berlin (1974)
Ruckmann, J.J., Tammer, K.: Linear-Quadratic Perturbations in One-Parametric Non-Linear Optimization. Systems Science, 18(1), 37–48 (1992)
Sawaragi, Y., Nakayama, H.,Tanino, T.: Theory of Multiobjective Optimization. Academic Press, New York, (1987)
Steuer, R.E.: Multiple Criteria Optimization: Theory, Computation and Applications, John Wiley, New York, (1986)
Tanino, T., Sawaragi, Y.: Duality Theory in Multiobjective Programming. Journal of Optimzation Theory and Applications, 27, 509–529 (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Enkhbat, R., Guddat, J., Chinchuluun, A. (2008). Parametric Multiobjective Optimization. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds) Pareto Optimality, Game Theory And Equilibria. Springer Optimization and Its Applications, vol 17. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77247-9_20
Download citation
DOI: https://doi.org/10.1007/978-0-387-77247-9_20
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-77246-2
Online ISBN: 978-0-387-77247-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)