Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S1195 - S1206|
|Published online||02 March 2021|
Optimality and duality in nonsmooth vector optimization with non-convex feasible set
Department of Mathematics, Miranda House, University of Delhi, New Delhi, Delhi 110007, India
2 Department of Mathematics, Atma Ram Sanatan Dharma College, University of Delhi, New Delhi, Delhi 110021, India
* Corresponding author: email@example.com
Accepted: 6 May 2020
For a convex programming problem, the Karush–Kuhn–Tucker (KKT) conditions are necessary and sufficient for optimality under suitable constraint qualification. Recently, Suneja et al. [Am. J. Oper. Res. 6 (2013) 536–541] proved KKT optimality conditions for a differentiable vector optimization problem over cones in which they replaced the cone-convexity of constraint function by convexity of feasible set and assumed the objective function to be cone-pseudoconvex. In this paper, we have considered a nonsmooth vector optimization problem over cones and proved KKT type sufficient optimality conditions by replacing convexity of feasible set with the weaker condition considered by Ho [Optim. Lett. 11 (2017) 41–46] and assuming the objective function to be generalized nonsmooth cone-pseudoconvex. Also, a Mond–Weir type dual is formulated and various duality results are established in the modified setting.
Mathematics Subject Classification: 90C29 / 90C46 / 90C30 / 90C26
Key words: Vector optimization / cones / generalized nonsmooth cone-pseudoconvex / KKT type optimality conditions / duality
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