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Sufficient optimality conditions and duality theorems for set-valued optimization problem under generalized cone convexity

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Abstract

In this paper, a new type of generalized cone convexity is introduced in the case of set-valued optimization problem where the maps involved are contingent epiderivable. It extends the notion of \(\rho -(\eta , \theta )\)-invexity from vector optimization to set-valued optimization. The sufficient Karush–Kuhn–Tucker (KKT) optimality conditions are investigated under the stated assumptions. We also study the duality results of Mond–Weir type (MWD), Wolfe type (WD) and mixed type (Mix D) for weak solutions of a pair of set-valued optimization problems.

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Acknowledgments

The authors are grateful to the reviewers for their valuable comments which improved the presentation of the paper. The first author is thankful to Council of Scientific and Industrial Research (CSIR), India, for his financial support in executing this study.

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  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur , 721302, West Bengal, India

    K. Das & C. Nahak

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  1. K. Das
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  2. C. Nahak
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Correspondence to C. Nahak.

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Das, K., Nahak, C. Sufficient optimality conditions and duality theorems for set-valued optimization problem under generalized cone convexity. Rend. Circ. Mat. Palermo 63, 329–345 (2014). https://doi.org/10.1007/s12215-014-0163-9

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  • DOI: https://doi.org/10.1007/s12215-014-0163-9

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