Jeyakumar, V.; Oettli, W.; Natividad, M. A solvability theorem for a class of quasiconvex mappings with applications to optimization. (English) Zbl 0791.46002 J. Math. Anal. Appl. 179, No. 2, 537-546 (1993). 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. Cited in 1 ReviewCited in 54 Documents 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 Keywords:solvability theorem; quasiconvex mappings; characterize the local and global solutions of optimization problems PDFBibTeX XMLCite \textit{V. Jeyakumar} et al., J. Math. Anal. Appl. 179, No. 2, 537--546 (1993; Zbl 0791.46002) Full Text: DOI