I use latest version of Mosek under cvx for solving mixed integer problem. The only variable inside my problem is binary vector, call it x. The objective is max \mu s.t \mu<=sum_log(wx) - vx(so it is a hypograph). w and v are vectors containing some weights, not a variable. There are some constraints on x and all of them are linear w.r.t. x. When I run it under cvx, Mosek outputs status “Unbounded”, but gives me a solution that is feasible and seems like correct. But I am still aware of the status. Did anyone encounter that problem before? Should I trust solution?
One idea that I have is that when Mosek starts its internal algorithm it chooses some initial point which is probably x = 0, so that objective becomes -Inf, so it reports “Unbounded” status. But this is only my guess.