I am trying to solve a small QP problem in CPLEX. The problem has several linear constraints. The optimiser runs and finds a solution which satisfies these constraints and CPLEX returns a success code.
However the value of the objective function given by this solution is greater than that for the solution if I just supply a vector of 1's (this is my initial state which I trying to improve upon).
So CPLEX is failing to revert to the initial solution even if that is better than the given solution. How can this be possible ? I have tested this in Excel using Excel solver and it does something similar so CPLEX is not the problem.
I had always assumed that QP problems possessed a unique solution. I believe that the QP problem has a positive semi-definite matrix. In fact I know that.
What am I doing incorrectly ? Here is the mps file: