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Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints

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Abstract

We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex sets defined by non necessarily convex functions, in terms of tangential subdifferentials. Our main result unifies a recent KKT type theorem obtained by Lasserre for differentiable functions with a nonsmooth version due to Dutta and Lalitha.

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References

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Acknowledgments

This research was supported by the MICINN of Spain, Grant MTM2011-29064-C03-01, and under Australian Research Council’s Discovery Projects funding scheme (project number DP140103213). The author is affiliated to MOVE (Markets, Organizations and Votes in Economics). I am grateful to two anonymous referees for their useful comments, which have helped me improve the presentation.

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  1. Departament d’Economia i d’Història Econòmica, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Juan Enrique Martínez-Legaz

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  1. Juan Enrique Martínez-Legaz
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Correspondence to Juan Enrique Martínez-Legaz.

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Martínez-Legaz, J.E. Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints. Optim Lett 9, 1017–1023 (2015). https://doi.org/10.1007/s11590-014-0822-y

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  • DOI: https://doi.org/10.1007/s11590-014-0822-y

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