Numerical Experiences with New Truncated Newton Methods in Large Scale Unconstrained Optimization

Recently, in [12] a very general class oftruncated Newton methods has been proposed for solving large scale unconstrained optimization problems. In this work we present the results of an extensive numericalexperience obtained by different algorithms which belong to the preceding class. This numerical study, besides investigating which arethe best algorithmic choices of the proposed approach, clarifies some significant points which underlies every truncated Newton based algorithm.

[1]  M. Saunders,et al.  Solution of Sparse Indefinite Systems of Linear Equations , 1975 .

[2]  Garth P. McCormick,et al.  A modification of Armijo's step-size rule for negative curvature , 1977, Math. Program..

[3]  Danny C. Sorensen,et al.  On the use of directions of negative curvature in a modified newton method , 1979, Math. Program..

[4]  B. Parlett.  The Symmetric Eigenvalue Problem , 1981 .

[5]  Richard H. Byrd,et al.  A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties. , 1985 .

[6]  R. Dembo,et al.  INEXACT NEWTON METHODS , 1982 .

[7]  Trond Steihaug,et al.  Truncated-newtono algorithms for large-scale unconstrained optimization , 1983, Math. Program..

[8]  Gene H. Golub,et al.  Matrix computations , 1983 .

[9]  S. Nash.  Newton-Type Minimization via the Lanczos Method , 1984 .

[10]  J. Cullum,et al.  Lanczos algorithms for large symmetric eigenvalue computations , 1985 .

[11]  L. Grippo,et al.  A truncated Newton method with nonmonotone line search for unconstrained optimization , 1989 .

[12]  L. Grippo,et al.  A class of nonmonotone stabilization methods in unconstrained optimization , 1991 .

[13]  Jorge Nocedal,et al.  A Numerical Study of the Limited Memory BFGS Method and the Truncated-Newton Method for Large Scale Optimization , 1991, SIAM J. Optim..

[14]  P. Toint,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[15]  Tamar Schlick,et al.  TNPACK—A truncated Newton minimization package for large-scale problems: I. Algorithm and usage , 1992, TOMS.

[16]  N. Deng,et al.  Nonmonotonic trust region algorithm , 1993 .

[17]  Nicholas I. M. Gould,et al.  CUTE: constrained and unconstrained testing environment , 1995, TOMS.

[18]  Michael C. Ferris,et al.  Nonmonotone curvilinear line search methods for unconstrained optimization , 1996, Comput. Optim. Appl..

[19]  Philippe L. Toint,et al.  An Assessment of Nonmonotone Linesearch Techniques for Unconstrained Optimization , 1996, SIAM J. Sci. Comput..

[20]  Philippe L. Toint,et al.  Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints , 1997, Math. Program..

[21]  Stefano Lucidi,et al.  Curvilinear Stabilization Techniques for Truncated Newton Methods in Large Scale Unconstrained Optimization , 1998, SIAM J. Optim..