Optimization Theory: Concepts, Methods, and Applications

Introduced by Polyak in 1966, the class of strongly quasiconvex functions includes some interesting nonconvex members, like the square root of the Euclidean norm or ratios with a nonnegative strongly convex numerator and a concave and positive denominator. In this talk, we survey the most relevant examples of strongly quasiconvex functions and results involving them available in the literature at the moment. In particular, we recall some recent algorithms for minimizing such functions, and hint toward some directions where additional investigations would be welcome. The talk is based on joint work with Felipe Lara, Raúl Marcavillaca, and Huu-Nhan Nguyen.