Efficient detection of hessian matrix sparsity pattern

Abstract

Evaluation of the Hessian matrix of a scalar function is a subproblem in many numerical optimization algorithms. For large-scale problems often the Hessian matrix is sparse and structured, and it is preferable to exploit such information when available. Using symmetry in the second derivative values of the components it is possible to detect the sparsity pattern of the Hessian via products of the Hessian matrix with specially chosen direction vectors. We use graph coloring methods and employ efficient sparse data structures to implement the sparsity pattern detection algorithms. Results from preliminary numerical testings are highly promising.