Characterizing quasiconvexity of the pointwise infimum of a family of arbitrary translations of quasiconvex functions, with applications to sums and quasiconvex optimization

Special Issue: Continuous Optimization and Stability Analysis

“…The authors give a constructive proof of the Hoffman's error bound and show that their method can calculate the constant at least in simple cases. • Flores-Bazán et al [13] show the existing relationship between two well-known statements saying that the sum and the minimum of two quasiconvex functions is not quasiconvex in general. To do that, the authors introduce and characterize the notion of quasiconvex family.…”