What function does Microsoft Solver Foundation's InteriorPointSolver minimize?

Question

I am attempting to use InteriorPointSolver to solve a standard Quadratic Programming problem with linear constraints (per the definition that can be found here). My problem has no linear term (the "c" vector in the definition). I am setting up the "Q" matrix by using SetCoefficient(Int32, Rational, Int32, Int32) across all my variables (passing the "goal" row as the vidRow). Am I correct in assuming that the InteriorPointSolver is minimizing the objective function as defined in the standard definition of the quadratic programming problem?

I ask this because when I calculate x^T * Q * x myself (using the optimal solution for x that I get from the solver), I get a value that is substantially different than what the solver claims the optimal objective function value is (via Statistics.Primal or GetValue(goal)). The only time my calculation and the solver's optimal value agree is when I use an identity matrix for Q. I am guessing that I am setting something up wrong or am not understanding exactly what function is being minimized.

I have consulted all the documentation I can find and cannot find a good explanation of exactly what function the interior point solver is minimizing. Can anyone guide me in the right direction?

Answer 1

As it turns out,

SetCoefficient(goal, 2.0, x, y)

Has exactly the same effect as

SetCoefficient(goal, 2.0, y, x)

The effect of both calls is to set the coefficient of the x*y term in your objective function, and the second call simply overwrites the coefficient that you set in the first call. The solver does not treat the xy term as distinct from the yx term, and does not add the coefficients (as I had expected). So, if your goal is to have a 4xy term in your objective function, you must make the following call:

SetCoefficient(goal, 4.0, x, y)

instead of the two calls listed above.