Javier Cano Cancela
Universidad Rey Julian Carlos
Improving directions of negative curvature for constrained problems in an efficient manner
In order to converge to second-order KKT points, second derivative information has to be taken into account. Therefore, methods for minimization satisfying convergence to second-order KKT points must, at least implicitly, compute a direction of negative curvature of an indefinite matrix. An important issue is to determine the quality of the negative curvature direction. This problem is closely related to the symmetric eigenvalue problem. More specifically we want to develop algorithms that improve directions of negative curvature with relatively little effort. This paper presents some methods to compute "good"
directions of negative curvature and we present numerical experiments that illustrate its practical effciency.