Abstract
We propose the notion of higher-order radial-contingent derivative of a set-valued map, develop some calculus rules and use them directly to obtain optimality conditions for several particular optimization problems. Then we employ this derivative together with contingent-type derivatives to analyze sensitivity for nonsmooth vector optimization. Properties of higher-order contingent-type derivatives of the perturbation and weak perturbation maps of a parameterized optimization problem are obtained.
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Acknowledgements
This research was supported by the Vietnam National University Hochiminh City (VNU-HCM) under the grant number B2013-28-01. A part of the work of the second author was completed during his stay as a visiting professor at the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose hospitality is gratefully acknowledged. The authors are indebted to the anonymous referees for many valuable detailed remarks, which have helped to improve significantly the paper.
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Diem, H.T.H., Khanh, P.Q. & Tung, L.T. On Higher-Order Sensitivity Analysis in Nonsmooth Vector Optimization. J Optim Theory Appl 162, 463–488 (2014). https://doi.org/10.1007/s10957-013-0424-3
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DOI: https://doi.org/10.1007/s10957-013-0424-3