Polar Conic Set-Valued Map in Vector Optimization. Continuity and Derivability

In the context of vector optimization, several results are stated mainly about the continuity and the derivability of a conic set-valued map (the polar conic function) having a close relation with the positive efficient points, the ideal points and other distinguished elements of the efficient line. The contingent cone to the set of the general positive quasiefficient points at a point x ₀ is also related with the frontier of the dual cone of the image at x ₀ of the polar conic function. This work was partially supported by Grant SEJ2006–15401–C04–02 of Spanish Ministerio de Ciencia y Tecnología and Grant S-0505/tic/0230-D3 of Comunidad Autónoma de Madrid. The authors are grateful to the referees for suggestions which led to improving the paper.