Opuscula Math. 34, no. 4 (), 665-682
http://dx.doi.org/10.7494/OpMath.2014.34.4.665
Opuscula Mathematica

# Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex functions

Abstract. In this paper, we generalize the notion of $$B$$-$$(p,r)$$-invexity introduced by Antczak in [A class of $$B$$-$$(p; r)$$-invex functions and mathematical programming, J. Math. Anal. Appl. 286 (2003), 187-206] for scalar optimization problems to the case of a multiobjective variational programming control problem. For such nonconvex vector optimization problems, we prove sufficient optimality conditions under the assumptions that the functions constituting them are $$B$$-$$(p,r)$$-invex. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem in the sense of Mond-Weir is given and several duality results are established under $$B$$-$$(p,r)$$-invexity.
Keywords: multiobjective variational control problems, efficient solution, $$B$$-$$(p,r)$$-invex functions, optimality conditions, duality.
Mathematics Subject Classification: 65K10, 90C29, 26B25.
Cite this article as:
Tadeusz Antczak, Manuel Arana Jiménez, Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex functions, Opuscula Math. 34, no. 4 (2014), 665-682, http://dx.doi.org/10.7494/OpMath.2014.34.4.665

Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.