An active set truncated Newton method for large-scale bound constrained optimization

An active set truncated Newton method for large-scale bound constrained optimization is proposed. The active sets are guessed by an identification technique. The search direction consists of two parts: some of the components are simply defined; the other components are determined by the truncated Newton method. The method based on a nonmonotone line search technique is shown to be globally convergent. Numerical experiments are presented using bound constrained problems in the CUTEr test problem library. The numerical performance reveals that our method is effective and competitive with the famous algorithm TRON.

[1]  Yunhai Xiao,et al.  Subspace Barzilai-Borwein Gradient Method for Large-Scale Bound Constrained Optimization , 2008 .

[2]  D. Bertsekas.  Projected Newton methods for optimization problems with simple constraints , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[3]  Francisco Facchinei,et al.  A Truncated Newton Algorithm for Large Scale Box Constrained Optimization , 2002, SIAM J. Optim..

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

[5]  L. Grippo,et al.  A nonmonotone line search technique for Newton's method , 1986 .

[6]  Francisco Facchinei,et al.  An Active Set Newton Algorithm for Large-Scale Nonlinear Programs with Box Constraints , 1998, SIAM J. Optim..

[7]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

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

[9]  J. J. Moré,et al.  On the identification of active constraints , 1988 .

[10]  Roger Fletcher,et al.  Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming , 2005, Numerische Mathematik.

[11]  Chih-Jen Lin,et al.  Incomplete Cholesky Factorizations with Limited Memory , 1999, SIAM J. Sci. Comput..

[12]  Ya-Xiang Yuan,et al.  A trust region method based on a new affine scaling technique for simple bounded optimization , 2013, Optim. Methods Softw..

[13]  William W. Hager,et al.  A New Active Set Algorithm for Box Constrained Optimization , 2006, SIAM J. Optim..

[14]  José Mario Martínez,et al.  Nonmonotone Spectral Projected Gradient Methods on Convex Sets , 1999, SIAM J. Optim..

[15]  D. Bertsekas.  Projected Newton methods for optimization problems with simple constraints , 1981, CDC 1981.

[16]  Nicholas I. M. Gould,et al.  Numerical methods for large-scale nonlinear optimization , 2005, Acta Numerica.

[17]  Chih-Jen Lin,et al.  Newton's Method for Large Bound-Constrained Optimization Problems , 1999, SIAM J. Optim..

[18]  J. Nocedal,et al.  A Limited Memory Algorithm for Bound Constrained Optimization , 1995, SIAM J. Sci. Comput..

[19]  V. Torczon,et al.  A GLOBALLY CONVERGENT AUGMENTED LAGRANGIAN ALGORITHM FOR OPTIMIZATION WITH GENERAL CONSTRAINTS AND SIMPLE BOUNDS , 2002 .