×

A solvability theorem for a class of quasiconvex mappings with applications to optimization. (English) Zbl 0791.46002

Summary: A solvability theorem is proved for a class of quasiconvex mappings. The solvability theorem is applied to characterize the local and global solutions of optimization problems where the mappings satisfy certain quasiconvexity conditions or their suitable approximations satisfy such conditions.

MSC:

46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
49J52 Nonsmooth analysis
46A55 Convex sets in topological linear spaces; Choquet theory
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
49J35 Existence of solutions for minimax problems
PDFBibTeX XMLCite
Full Text: DOI