Second-order algorithms for generalized finite and semi-infinite min-max problems

Abstract

We present two second-order algorithms, one for solving a class of finite generalized min-max problems and one for solving semi-infinite generalized min-max problems. Our algorithms make use of optimality functions based on second-order approximations to the cost function and of corresponding search direction functions. Under reasonable assumptions we prove that both of these algorithms converge Q-superlinearly, with rate at least 3/2. This paper is a continuation of [E. Polak, L. Qi, and D. Sun, Comput. Optim. Appl., 13 (1999), pp. 137–161].