On Necessary Optimality Conditions for Nonsmooth Vector Optimization Problems with Mixed Constraints in Infinite Dimensions


DOI: 10.1007/s00245-016-9383-z

Cite this article as:
Tuan, N.D. Appl Math Optim (2016). doi:10.1007/s00245-016-9383-z


In this note, we develop first- and second-order necessary optimality conditions for local weak solutions in nonsmooth vector optimization problems subject to mixed constraints in infinite-dimensional settings. To this aim, we use some set-valued directional derivatives of the Hadamard type and tangent sets, and impose (first-order) Hadamard differentiability assumptions of the data at the point of consideration.


Nonsmooth vector optimizationnecessary optimality conditionsweak solutionssecond-order tangent setssecond-order directional derivatives

Mathematics Subject Classification


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Economics-Ho Chi Minh CityHo Chi Minh CityVietnam