Variational Principles in Analysis and Existence of Minimizers for Functions on Metric Spaces
Aram Vladimirovich Arutyunov, Sergey Evgenyevich Zhukovskiy · SIAM Journal on Optimization · 2019
Functions defined on metric spaces are studied. For these functions, a generalized Caristi-like condition is introduced. It is shown that this condition is sufficient for a bounded below, lower semicontinuous function to attain its minimum. Criteria for a generalized Caristi-like condition to hold are derived. Generalizations of the Ekeland and Bishop--Phelps variational principles are obtained and compared with their prototypes.