Generalized quasiconvex set-valued maps

Authors

  • Nicolae Popovici “Babes-Bolyai” University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat312-725

Keywords:

generalized quasiconvexity, set-valued maps, scalarization
Abstract views: 187

Abstract

The aim of this paper is to introduce a concept of quasiconvexity for set-valued maps in a general framework, by only considering an abstract convexity structure in the domain and an arbitrary binary relation in the codomain. It is shown that this concept can be characterized in terms of usual quasiconvexity of certain real-valued functions. In particular, we focus on cone-quasiconvex set-valued maps with values in a partially ordered vector space.

Downloads

Download data is not yet available.

References

Aubin, J.-P. and Frankowska, H., Set-Valued Analysis, Birkhäuser, Boston, 1990.

Borwein, J. M., Multivalued convexity and optimization: A unified approach to inequality and equality constraints, Math. Programming, 13, pp. 183-199, 1977, https://doi.org/10.1007/BF01584336 DOI: https://doi.org/10.1007/BF01584336

Benoist, J., Borwein, J. M. and Popovici, N., A characterization of quasiconvex vector valued functions, Proc. Amer. Math. Soc., 131, pp. 1109-1113, 2003, https://doi.org/10.1090/S0002-9939-02-06761-8 DOI: https://doi.org/10.1090/S0002-9939-02-06761-8

Jahn, J., Mathematical Vector Optimization in Partially Ordered Linear Spaces, Peter Lang Verlang, Frankfurt, 1986.

Kuroiwa, D., Convexity for set-valued maps, Appl. Math. Lett., 9, pp. 97-101, 1996, https://doi.org/10.1016/0893-9659(96)00020-1 DOI: https://doi.org/10.1016/0893-9659(96)00020-1

Luc, D. T., Theory of Vector Optimization, Lecture Notes in Econ. and Math. Systems, Vol. 319, Springer-Verlag, Berlin, 1989. DOI: https://doi.org/10.1007/978-3-642-50280-4

Luc, D. T., On three concepts of quasiconvexity in vector optimization, Acta Mathematica Vietnamica, 15, no. 1, pp. 3-9, 1990.

Popovici, N., Generalized quasiconvexity via properly characteristic functions associated to binary relations, Acta Mathematica Vietnamica, 26, no. 2, pp. 169-175, 2001.

Rubinov, A., Abstract Convexity and Global Optimization, Kluwer Academic Publishers, Dordrecht, 2000. DOI: https://doi.org/10.1007/978-1-4757-3200-9

Downloads

Published

2002-08-01

How to Cite

Popovici, N. (2002). Generalized quasiconvex set-valued maps. Rev. Anal. Numér. Théor. Approx., 31(2), 199–206. https://doi.org/10.33993/jnaat312-725

Issue

Section

Articles