I am not sure if this is the right place to ask this question, please point me to the correct forum if I posted in a wrong place.
I have an optimization problem like this
Max x2 - x1 st x1x2 <= 0 x1^2 + x2^2 <= 9 x1 and x2 are integers
What can I do to transform this problem into a convex optimization problem (the 1st constraint)? Or to a linear Integer programming problem? Because I only know algorithms for solving problems in those two categories. Please help.
Edit: My intention was to know if there are any common ways to transform the 1st constraint into some convex constraints. The domain of the original problem is huge and it has 10s of dimensions that you cannot draw the functions to get the answer. Lets say the problem look like this (please forgive me, i don't know how to use Latex ...)
Min sum(yi) st sum on j(wij) <= cyi for all i in N sum on i(xij) = 1 for all j in N wij = wjxij for all i, j in N Lij = Ljxij for all i, j in N Dij = Lij + wij for all i, j in N (Lij - Dik)(Lik - Dij) <= 0 for all i, j, k in N Aj <= Lj for all j in N Lj <= Aj + Qj for all j in N xij = 0 or 1 for all i, j in N yi = 0 or 1 for all i in N Wj, Lj, Qj and c are constant N = 10000
Other than using implicit enumeration, what can i do? The only constraint that is not convex is this one
(Lij - Dik)(Lik - Dij) <= 0 for all i, j, k in N