matrix storage

The \(n\) by \(n\) objective Hessian matrix \(H\), the \(n\) by \(n\) constraint Hessians \((H_c)_i\), \(i = 1, \ldots, m\) and the \(m\) by \(n\) constraint Jacobian \(A\) will be available in a sparse co-ordinate storage format.

Only the nonzero entries of the matrices are stored. For the \(l\)-th entry of \(A\), its row index \(i\), column index \(j\) and value \(a_{ij}\) are stored in the \(l\)-th components of the integer arrays A_row, A_col and real array A_val, respectively. The order is unimportant, but the total number of entries A_ne is also required.

The same scheme is applicable to \(H\) (thus requiring integer arrays H_row, H_col, a real array H_val and an integer value H_ne), except that only the entries in the lower triangle need be stored.

For the constraint Hessians, a third index giving the constraint involved is required for each entry, and is stored in the integer array H_ptr. Once again, only the lower traingle is stored.