This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the $l$-type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms of a high-order directional derivative of set-valued maps and the (convex or limiting) subdifferentials, normal cones and coderivatives. Various illustrating examples are presented.
Citation
To appear in Journal of Optimization Theory and Applications