Transformation of quasiconvex functions to eliminate local minima
It is proved that any lower semicontinuous quasiconvex function \(f\) may be written as a composition of two functions \(f = h~ o~ g\), where \(h\) is nondecreasing and \(g\) is quasiconvex and each of its local minimum is at the same time its global minimum. Therefore, the minimization of any lower semicontinuous quasiconvex function \(f\) can be reduced to the minimization of the function \(g\), whose local and global minima coincide. The authors prove this result by making use of some continuity properties of so-called ``adjusted sublevel sets'' and ``sublevel set operators''. The results of the paper make the minimization of lower semicontinuous quasiconvex functions easier.
scientific article; zbMATH DE number 6882321
scientific article