Abstract

We present sufficient conditions to guarantee the existence of solutions for nonconvex semi-infinite optimization problems. These conditions are also employed to establish the lower semicontinuity of the value function at 0. Furthermore, we extend classical results from convex analysis to characterize the global properties of quasiconvex functions based on their behavior at individual points. Our findings generalize and complement existing approaches, addressing problems that extend beyond the scope of previous results. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.