The original publication is available at www.springerlink.comThe efficient combination of directions is a significant problem in line search methods that either use negative curvature, or wish to include additional information such as the gradient or different approximations
to the Newton direction.
In this paper we describe a new procedure to combine several of these directions within an interior-point primal-dual algorithm. Basically, we combine in an efficient manner a modified Newton direction with the
gradient of a merit function and a direction of negative curvature, if it exists.We also show that the procedure
is well-defined, and it has reasonable theoretical properties regarding the rate of convergence of the method.
We also present numerical results from an implementation of the proposed algorithm on a set of small
test problems from the CUTE collection.Research supported by Spanish MEC grants BEC2000-0167 and PB98-0728Publicad
