Originally posted by: Optimiser

I am trying to solve an MIQP with a non-convex quadratic objective, linear constraints, and continuous variables, calling cplex 12.6.3 from Matlab. I have a valid feasible solution for it, which I'd like to pass as a MipStart.

The first problem is that if I don't specify Model.ctype = 'C...C' (since it's the default), then the MipStart seems to be ignored.

Second, if I explicitly specify the all-continuous ctype, then the MipStart is processed, but I get the warning "No solution found from 1 MIP starts." I know that the MipStart is correct, because it happens to be an integer vector, and if I change ctype to the all-integer 'I...I', then I get the expected "1 of 1 MIP starts provided solutions." Also, refineMipStartConflict(1) says that there is no conflict. The issue seems to be specifically with non-convex quadratic objectives combined with the presence of continuous variables. Below is a minimal example.

I'd appreciate any help; thanks!

prob.f = [0;0] ;
prob.Aeq = [1 1];
prob.beq = 1;
prob.lb = [-10; -10];
prob.ub = [10; 10];
prob.H = [0 1; 1 1];
cp = Cplex(prob);
cp.MipStart(1).x = [1; 0];
cp.Model.ctype = 'CC';
cp.Param.optimalitytarget.Cur = 3; % global opt
sol = cp.solve()