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Abstract and Applied Analysis
Volume 2018, Article ID 5962049, 6 pages
Research Article

Necessary and Sufficient Conditions for Set-Valued Maps with Set Optimization

Faculté des Sciences et Techniques, Université Cadi Ayyad, BP 549, Marrakech, Morocco

Correspondence should be addressed to Abdessamad Oussarhan; moc.liamg@assuo.damassedba

Received 15 August 2017; Accepted 10 December 2017; Published 1 January 2018

Academic Editor: Patricia J. Y. Wong

Copyright © 2018 Abdessamad Oussarhan and Ikram Daidai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Optimality conditions are studied for set-valued maps with set optimization. Necessary conditions are given in terms of -derivative and contingent derivative. Sufficient conditions for the existence of solutions are shown for set-valued maps under generalized quasiconvexity assumptions.