Mathematical Programming

, Volume 96, Issue 3, pp 529–559 | Cite as

Combining search directions using gradient flows

  • Javier M. Moguerza
  • Francisco J. Prieto


 The 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.


Test Problem Search Method Significant Problem Search Direction Line Search 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Javier M. Moguerza
    • 1
  • Francisco J. Prieto
    • 2
  1. 1.School of Engineering, Univ. Rey Juan Carlos, Madrid, Spain, e-mail: Research supported by Spanish MEC grant TIC2000-1750-C06-04 and CAM project 07T/0005/2001ES
  2. 2.Dept. of Statistics and Econometrics, Univ. Carlos III de Madrid, Spain, e-mail: Research supported by Spanish MEC grants BEC2000-0167 and PB98-0728ES

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