The full form of QMC is Quadratic Matrix Constraint.

In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions. It has the form

where P₀, …, P_m are n-by-n matrices and x ∈ Rⁿ is the optimization variable.

If P₀, …, P_m are all positive semidefinite, then the problem is convex. If these matrices are neither positive nor negative semidefinite, the problem is non-convex. If P₁, … ,P_m are all zero, then the constraints are in fact linear and the problem is a quadratic program.