Procedures in Online Documentation
The QP solver in the OPTMODEL procedure implements an infeasible primaldual predictorcorrector interior point algorithm that enables you to solve quadratic programming problems.
Mathematically, a quadratic programming problem can be stated as
where


is the quadratic (also known as Hessian) matrix 


is the constraints matrix 


is the vector of decision variables 


is the vector of linear objective function coefficients 


is the vector of constraints righthand sides (RHS) 


is the vector of lower bounds on the decision variables 


is the vector of upper bounds on the decision variables 
The quadratic matrix is assumed to be symmetric; that is,
Indeed, even if , then the simple modification
produces an equivalent formulation hence symmetry is assumed. When you specify a quadratic matrix, it suffices to list only lower triangular coefficients.
In addition to being symmetric, is also required to be positive semidefinite
for minimization models; it is required to be negative semidefinite for maximization models. Convexity can come as a result of a matrixmatrix multiplication
or as a consequence of physical laws, and so on.