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Existence and characterization theorems in nonconvex vector optimization

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  • Nergiz Kasimbeyli

Abstract

This paper presents existence conditions and characterization theorems for minimal points of nonconvex vector optimization problems in reflexive Banach spaces. Characterization theorems use special class of monotonically increasing sublinear scalarizing functions which are defined by means of elements of augmented dual cones. It is shown that the Hartley cone-compactness is necessary and sufficient to guarantee the existence of a properly minimal point of the problem. The necessity is proven in the case of finite dimensional space. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Nergiz Kasimbeyli, 2015. "Existence and characterization theorems in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 62(1), pages 155-165, May.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:1:p:155-165
    DOI: 10.1007/s10898-014-0234-7
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    References listed on IDEAS

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    1. Jonathan M. Borwein, 1983. "On the Existence of Pareto Efficient Points," Mathematics of Operations Research, INFORMS, vol. 8(1), pages 64-73, February.
    2. Refail Kasimbeyli, 2013. "A conic scalarization method in multi-objective optimization," Journal of Global Optimization, Springer, vol. 56(2), pages 279-297, June.
    3. Dinh The Luc, 1989. "An Existence Theorem in Vector Optimization," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 693-699, November.
    4. K.F. Ng & X.Y. Zheng, 2002. "Existence of Efficient Points in Vector Optimization and Generalized Bishop–Phelps Theorem," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 29-47, October.
    5. Ozdemir, Mujgan S. & Gasimov, Rafail N., 2004. "The analytic hierarchy process and multiobjective 0-1 faculty course assignment," European Journal of Operational Research, Elsevier, vol. 157(2), pages 398-408, September.
    6. Gasimov, Rafail N. & Sipahioglu, Aydin & Sarac, Tugba, 2007. "A multi-objective programming approach to 1.5-dimensional assortment problem," European Journal of Operational Research, Elsevier, vol. 179(1), pages 64-79, May.
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    Cited by:

    1. Refail Kasimbeyli & Masoud Karimi, 2021. "Duality in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 139-160, May.

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