An aggregate deformation homotopy method for min‐max‐min problems with max‐min constraints

In this paper, the constrained min‐max‐min problem, which is an essentially nonsmooth and nonconvex problem, is considered. Based on a twice aggregate function with a modification, an aggregate deformation homotopy method is established. Under some suitable assumptions, a smooth path from a randomly given point to a solution of the generalized KKT system is proven to exist. By numerically tracing the smooth path, a globally convergent algorithm for some solution of the problem is given. Some numerical results are given to show the feasibility of the method.