Factorizing the all 1's matrix as a product of three 0-1 matrices using gradient descent

[@vitordelima]

I thought gradient descent would never find an exact solution for it. If this can be generalized to other cases such as integer or mixed linear programming it could simplify many optimization problems.

[@josephvanname3377]

I have been using gradient descent to solve the typical case of other NP-complete optimization problems such as 3-satisfiability, and the clique problem (or more generally the submatrix sum or submatrix spectral radius maximization problem). For the clique problem and submatrix maximization problem, I was able to use my own notion of an LSRDR to obtain the solution (I made animations about this). For integer programming, one can use the penalty function f(sin(pi*x)^2) where f is monotonic to make x an integer, but I am unsure about how easily this sort of penalty function could be used for solving integer programming functions.

[@vitordelima]

@@josephvanname3377 I don't know the details but there are other optimization methods for large problems besides gradient descent, since those problems seem to have a more "erratic" nature maybe those alternative methods could be useful.

[@robvdm]

Need to reduce the step size…

[@josephvanname3377]

But it still solves the problem. And we need these things to behave unexpectedly some times because that is more fun.