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Extremal Systems for Sets and Multifunctions in Multiobjective Optimization with Variable Ordering Structures

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Abstract

In this paper, we study extremal systems for sets and multifunctions in multiobjective optimization with variable/nonconstant ordering structures, which reduce to vector optimization when an ordering structure is constant, i.e., it is defined by a fixed ordering cone/set. It is important to mention that we do not impose either convexity or nonempty interiority property on ordering structures. Based on these systems, we derive verifiable necessary conditions for nondominated solutions to multiobjective problems with geometric constraints. Examples are provided to illustrate the usage of the obtained results.

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Acknowledgments

The authors are gratefully indebted to the anonymous referee for their helpful remarks.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI, 49855, USA

    Truong Q. Bao

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  1. Truong Q. Bao
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Correspondence to Truong Q. Bao.

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Dedicated to Professor Boris Mordukhovich on the occasion of his 65th birthday.

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Bao, T.Q. Extremal Systems for Sets and Multifunctions in Multiobjective Optimization with Variable Ordering Structures. Vietnam J. Math. 42, 579–593 (2014). https://doi.org/10.1007/s10013-014-0099-6

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  • DOI: https://doi.org/10.1007/s10013-014-0099-6

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