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Generalized nonsmooth cone convexity in terms of convexifactors in vector optimization

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Abstract

In this paper, we introduce new classes of K-∂*pseudoconvex, K-∂* quasiconvex and other related functions in terms of convexifactors where K is a closed convex cone with non empty interior. We study their relations with other similar functions existing in literature. We derive necessary and sufficient optimality conditions for a vector optimization problem over cones by using these functions and establish various duality results by associating a dual problem to it.

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Acknowledgments

The authors wish to thank Dr. Joydeep Dutta for valuable suggestions during the preparation of the paper. The authors are thankful to the unknown referee for his helpful comments which has improved the quality of presentation of the paper. The first author is grateful to U.G.C. for providing financial support.

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  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    S. K. Suneja & Bhawna Kohli

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  1. S. K. Suneja
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  2. Bhawna Kohli
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Correspondence to Bhawna Kohli.

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Suneja, S.K., Kohli, B. Generalized nonsmooth cone convexity in terms of convexifactors in vector optimization. OPSEARCH 50, 89–105 (2013). https://doi.org/10.1007/s12597-012-0092-3

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