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Jahn-Graef-Younes type algorithms for discrete vector optimization based on cone-monotone sorting functions

Christian GŁnther(Christian.Guenther***at***mathematik.uni-halle.de)
Nicolae Popovici(popovici***at***math.ubbcluj.ro)

Abstract: In this paper we present new Jahn-Graef-Younes type algorithms for solving discrete vector optimization problems. In order to determine all minimal elements of a finite set with respect to an ordering cone, the original approach proposed by Jahn in 2006 (known as the Jahn-Graef-Younes method) consists of a forward iteration (Graef-Younes method), followed by a backward iteration. Our methods involve additional sorting procedures based on scalar cone-monotone functions. In particular, we analyze the case where the ordering cone is polyhedral. Computational results, obtained in MATLAB, allow us to compare our new algorithms with the original Jahn-Graef-Younes method.

Keywords: Multiobjective optimization; Discrete optimization; Minimal elements; Domination property; Jahn-Graef-Younes method; Cone-monotone functions

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Preprint (June 16, 2017), Martin Luther University Halle-Wittenberg, Faculty of Natural Sciences II, Institute for Mathematics, 06099 Halle (Saale), Germany (submitted)

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Entry Submitted: 06/19/2017
Entry Accepted: 06/19/2017
Entry Last Modified: 06/19/2017

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