If the Hessian matrix Q is positive definite, then a global solution is found. When Q is indefinite, a Kuhn-Tucker point that is usually a local solution is found.
Feasibility is obtained by minimizing a sum of constraint violations.
The Devex method for avoiding near-zero pivots is used to promote stability. The matrix algebra is implemented so that the algorithm can take advantage of sparse factors of the basis matrix. Factors of the reduced Hessian matrix are stored in a dense format, an approach that is most effective when the number of free variables is relatively small. The user must supply a subroutine to evaluate the Hessian matrix Q , so that sparsity in Q can be exploited. The code is written to take maximum advantage of this situation, so that it also provides an efficient method for linear programming.