Numerical methods for solving unimodal multiple criteria optimization problems - a synthesis

Liana Lupşa; Ioana Chiorean

doi:10.33993/jnaat371-876

Authors

Liana Lupşa Babeş-Bolyai University, Cluj-Napoca, Romania
Ioana Chiorean Babeş-Bolyai University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat371-876

Keywords:

generalized unimodal functions, minimum points, multiple criteria programming, efficient points, weakly efficient points, serial and parallel calculus

Abstract views: 214

Abstract

In this paper we give a general method to approximate the set of all efficient solutions and the set of all weakly-efficient solutions for a multiple criteria optimization problem involving generalized unimodal objective functions on the feasible sets. This type of problems appear frequently in Economy, Mathematics, sometimes in Medico-Economics studies, etc.

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References

Björklund, H., Sandberg, S., Vorobyov, S., An Experimental Study of Algorithms for Completely Unimodal Optimization. Technical report 2002-030, October 2002. Department of Information Technology. Uppsala University.

Chiorean, I., Parallel calculus, Cluj-Napoca, Editura Microinformatica, 2000 (in Romanian).

Chiorean, I., Lupsa, L. and Popovici, N., A Fibonacci type method for determine the set of efficient points of an unimodal multicriteria optimization, Creative Math. & Inf., 16, pp. 114-123, 2007.

Demaine, E.D., Langerman, St., Optimizing a 2D Function Satisfying Unimodality Properties, https://doi.org/10.1007/11561071_78 DOI: https://doi.org/10.1007/11561071_78

Karmanov, V. G., Programmation mathématique, Editions Mir, Moscou, 1977.

Luc, D. T., Theory of Vector Optimization, Springer-Verlag, Berlin, 1989. DOI: https://doi.org/10.1007/978-3-642-50280-4

Lupşa, L. and Blaga, L. R., Optimum points and integer unimodal functions, Automation Computers Applied Mathematics, 13, no. 1, pp. 121-130, 2004, https://doi.org/10.1016/j.compstruc.2003.10.003 DOI: https://doi.org/10.1016/j.compstruc.2003.10.003

Lupşa, L., Popovici, N., A new algorithm for solving multicriteria unimodal optimization problems. Ann. Tiberiu Popoviciu Sem. Functional Equations, Approximation Convexity, 3, pp. 123-130, 2005. DOI: https://doi.org/10.1080/02331930500096213

Lupşa, L., Popovici, N., Generalized Unimodal Multicriteria Optimization, Rev. Anal. Numér. Théor Approx., 35, pp. 65-70, 2006, http://ictp.acad.ro/jnaat/journal/article/view/2006-vol35-no1-art9

Popovici, N., Multicriteria optimization with unimodal objective functions, Approximation and Optimization, Proceedings of the International Conference on Approximation and Optimization, Romania, ICAOR, Cluj-Napoca, July 29 - August 1, Vol. 1, pp. 341-344, 1996.