A note on exploiting structure when using slack variables

We show how to exploit the structure inherent in the linear algebra for constrained nonlinear optimization problems when inequality constraints have been converted to equations by adding slack variables and the problem is solved using an augmented Lagrangian method.

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

[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]  Michael A. Saunders,et al.  MINOS/AUGMENTED User's Manual. , 1980 .

[4]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[5]  P. Toint,et al.  Global convergence of a class of trust region algorithms for optimization with simple bounds , 1988 .

[6]  M. J. D. Powell,et al.  A method for nonlinear constraints in minimization problems , 1969 .

[7]  Nesa L'abbe Wu,et al.  Linear programming and extensions , 1981 .

[8]  Nicholas I. M. Gould,et al.  Convergence Properties of Minimization Algorithms for Convex Constraints Using a Structured Trust Region , 1996, SIAM J. Optim..

[9]  Michael A. Saunders,et al.  Large-scale linearly constrained optimization , 1978, Math. Program..

[10]  Philippe L. Toint,et al.  Towards an efficient sparsity exploiting newton method for minimization , 1981 .

[11]  Jorge J. Moré,et al.  Trust regions and projected gradients , 1988 .

[12]  Nicholas I. M. Gould,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[13]  H. C. Williams,et al.  Advanced Linear Programming , 1983, The Mathematical Gazette.

[14]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[15]  Philip E. Gill,et al.  Practical optimization , 1981 .

[16]  Margaret H. Wright,et al.  Interior methods for constrained optimization , 1992, Acta Numerica.