While analysing a particular iterative method which reaches the fixed points of a multivariate function f(x, y) (x and y are N-dimensional vectors in this case), I was able to reformulate it in the following terms
that is, as some kind of 'alternating' descent, in which x goes in the direction which minimizes y, and vice-versa. Has anyone ever seen something like that, e.g. some algorithm which performs this kind of update?
Actually the 2nd equation has a + instead of a -, so one equation would be performing a descent while the other one performs a ascent... But I am interested in any kind of algorithm which does this kind of alternation.