Opuscula Math. 34, no. 4 (2014), 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

Tadeusz Antczak
Manuel Arana Jiménez

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.

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  • Tadeusz Antczak
  • University of Łódź, Faculty of Mathematics, Banacha 22, 90-238 Łódź, Poland
  • Manuel Arana Jiménez
  • Universidad de Cádiz, Facultad de CCSS y de la Comunicación, Departamento de Estadística e Investigación Operativa, Spain
  • Received: 2013-11-06.
  • Revised: 2014-04-16.
  • Accepted: 2014-04-27.
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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

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