I have an optimization task, and I am looking for a method (preferably using Mathematica built in functions and routines) for solving this and similar problems.
Let there be two functions: f1(x1,⋯,xn,y1,⋯,yn) and f2(x1,⋯xn,y1,⋯,yn).
Maximize f1 with regards to variables x1,⋯,xn with y1,⋯,yn fixed at the values that maximizes f2.
Maximize f2 with regards to variables y1,⋯,yn with x1,⋯,xn fixed at the values that maximizes f1.
Both functions are continuous, with continuous first, second (higher?) derivatives.