Detecting negative eigenvalues of exact and approximate Hessian matrices in optimization

Nonconvex minimization algorithms often benefit from the use of second-order information as represented by the Hessian matrix. When the Hessian at a critical point possesses negative eigenvalues, the corresponding eigenvectors can be used to search for further improvement in the objective function value. Computing such eigenpairs can be computationally challenging, particularly if the Hessian matrix … Read more