Inexact semimonotonic augmented lagrangians with optimal feasibility convergence for convex bound and equality constrained quadratic programming

SIAM Journal on Numerical Analysis

Volumn 43, Issue 1, 2005, Pages 96-115

  Dostal Z ^a  

^a VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

Author keywords

Adaptive precision control; Augmented Lagrangians; Box and equality constraints; Quadratic programming

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

ADAPTIVE PRECISION CONTROL; AUGMENTED LAGRANGIANS; BOX AND EQUALITY CONSTRAINTS;

LAGRANGE MULTIPLIERS;

EID: 33644554487     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903436393     Document Type: Article

References (30)

1. PH. AVERY, G. REBEL, M. LESOINNE, AND C. FARHAT, A numerically scalable dual-primal substructuring method for the solution of contact problems - part I: The frictionless case, Computer Methods in Applied Mechanics and Engineering, 193 (2004), pp. 2403-2426.
2. D. P. BERTSEKAS, Constrained Optimization and Lagrange Multiplier Methods, Academic Press, London, 1982.
3. D. P. BERTSEKAS, Nonlinear Optimization, Athena Scientific, Belmont, 1999.
4. E. G. BIRGIN AND J. M. MARTINEZ, Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients, Comput. Optim. Appl., 23 (2002), pp. 101-125.
5. A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal., 28 (1991), pp. 545-572.
6. A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, LANCELOT: A Fortran Package for Large Scale Nonlinear Optimization, Springer-Verlag, Berlin, 1992.
7. Z. DOSTÁL, Duality based domain decomposition with proportioning for the solution of free boundary problems, J. Comput. Appl. Math., 63 (1995), pp. 203-208.
8. Z. DOSTÁL, Box constrained quadratic programming with proportioning and projections, SIAM J. Optim., 7 (1997), pp. 871-887.
9. Z. DOSTÁL, On preconditioning and penalized matrices, Numer. Linear Algebra Appl., 6 (1999), pp. 109-114.
10. Z. DOSTÁL, A proportioning based algorithm for bound constrained quadratic programming with the rate of convergence, Numer. Algorithms, 34 (2003), pp. 293-302.
11. Z. DOSTÁL, Semi-monotonic inexact augmented Lagrangians for quadratic programming with equality constraints, Optim. Methods Softw., to appear.
12. Z. DOSTÁL, A. FRIEDLANDER, AND S. A. SANTOS, Solution of Coercive and Semicoercive Contact Problems by FETI Domain Decomposition, Contemp. Math. 218, AMS, Providence, RI, 1998, pp. 83-93.
13. Z. DOSTÁL, A. FRIEDLANDER, AND S. A. SANTOS, Augmented Lagrangians with adaptive precision control for quadratic programming with equality constraints, Comput. Optim. Appl., 14 (1999), pp. 37-53.
14. Z. DOSTÁL, F. A. M. GOMES, AND S. A. SANTOS, Duality based domain decomposition with natural coarse space for variational inequalities, J. Comput. Appl. Math., 126 (2000), pp. 397-415.
15. Z. DOSTÁL, A. FRIEDLANDER, AND S. A. SANTOS, Augmented Lagrangians with adaptive precision control for quadratic programming with simple bounds and equality constraints, SIAM J. Optim., 13 (2003), pp. 1120-1140.
16. Z. DOSTÁL, F. A. M. GOMES NETO, AND S. A. SANTOS, Solution of contact problems by FETI domain decomposition with natural coarse space projection, Comput. Meth. Appl. Mech. Eng., 190 (2000), pp. 1611-1627.
17. Z. DOSTÁL AND D. HORÁK, Scalability and FETI based algorithm for large discretized variational inequalities, Math. Comput. Simulation, 61 (2003), pp. 347-357.
18. Z. DOSTÁL AND D. HORÁK, Scalable FETI with Optimal Dual Penalty for a Variational Inequality, Numer. Linear Algebra Appl., 11 (2004), pp. 455-472.
19. Z. DOSTÁL AND D. HORÁK, Scalable FETI with Optimal Dual Penalty for Semicoercive Variational Inequalities, Contemp. Math. 329, AMS, Providence, RI, 2003, pp. 79-88.
20. Z. DOSTÁL, D. HORÁK, AND D. STEFANICA, A scalable FETI-DP algorithm for coercive variational inequalities, IMACS J. Appl. Numer. Anal., to appear.
21. Z. DOSTÁL AND J. SCHÖBERL, Minimizing quadratic functions subject to bound constraints with the rate of convergence and finite termination, Comput. Optim. Appl., 30 (2005), pp. 23-44.
22. C. FARHAT, J. MANDEL, AND F.-X. Roux, Optimal convergence properties of the FETI domain decomposition method, Comput. Methods Appl. Mech. Eng., 115 (1994), pp. 365-385.
23. A. FRIEDLANDER, J. M. MARTÍNEZ, AND M. RAYDAN, A new method for large scale box constrained quadratic minimization problems, Optim. Methods Softw., 5 (1995), pp. 57-74.
24. R. GLOWINSKI AND P. LE TALLEC, Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics, SIAM Stud. Appl. Math. 9, SIAM, Philadelphia, 1989.
25. W. W. HAGER, Analysis and implementation of a dual algorithm for constraint optimization, J. Optim. Theory Appl., 79 (1993), pp. 37-71.
26. M. R. HESTENES, Multiplier and gradient methods, J. Optim. Theory Appl., 4 (1969), pp. 303-320.
27. R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
28. M. J. D. POWELL, A Method for Nonlinear Constraints in Minimization Problems, R. Fletcher, ed., Academic Press, New York, 1969, pp. 283-298.
29. J. SCHÖBERL, Solving the Signorini problem on the basis of domain decomposition techniques, Computing, 60 (1998), pp. 323-344.
30. S. J. WRIGHT, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, 1997.