Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2014), Article ID 524698, 12 pages.

Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

Sheng-lan Chen, Nan-Jing Huang, and Donal O'Regan

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Abstract

We introduce a class of functions called geodesic B -preinvex and geodesic B -invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B -preinvex and geodesic quasi/pseudo B -invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B -preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B -invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.

Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 524698, 12 pages.

Dates
First available in Project Euclid: 1 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1412177577

Digital Object Identifier
doi:10.1155/2014/524698

Mathematical Reviews number (MathSciNet)
MR3191123

Zentralblatt MATH identifier
07010666

Citation

Chen, Sheng-lan; Huang, Nan-Jing; O'Regan, Donal. Geodesic B -Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds. J. Appl. Math. 2014, Special Issue (2014), Article ID 524698, 12 pages. doi:10.1155/2014/524698. https://projecteuclid.org/euclid.jam/1412177577


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