An active set Newton algorithm for large-scale nonlinear programs with box constraints

SIAM Journal on Optimization

Volumn 8, Issue 1, 1998, Pages 158-186

  Facchinei, Francisco ^a   Júdice, Joaquim ^b   Soares, Joao ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF COIMBRA   (Portugal)

^c Columbia University ^*  (United States)

Author keywords

Active set; Box constraints; Large scale problems; Newton's method

Indexed keywords

EID: 0038342659     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623493253991     Document Type: Article

References (38)

1. B. AVERICK, R. CARTER, J. MORÉ, AND G.-L. XUE, The Minpack-2 Test Problem Collection, Tech. report MCS-P153-0692, Argonne National Laboratory, Mathematics and Computer Science Division, Argonne, IL, June 1992.
2. D. BERTSEKAS, On the Goldstein-Levitin-Polyak gradient projection method, IEEE Trans. Automat. Control, AC-21 (1976), pp. 174-184.
3. D. BERTSEKAS, Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, 1982.
4. D. BERTSEKAS, Projected Newton methods for optimization problems with simple constraints, SIAM J. Control Optim., 20 (1982), pp. 221-246.
5. I. BONGARTZ, A. CONN, N. GOULD, AND P. TOLNT, CUTE: Constrained and unconstrained testing environment, ACM Trans. Math. Software, 21 (1995), pp. 123-160.
6. J. BURKE AND J. MORÉ, On the identification of active constraints, SIAM J. Numer. Anal., 25 (1988), pp. 1197-1211.
7. J. BURKE AND J. MORÉ, Exposing constraints, SIAM J. Optim., 4 (1994), pp. 573-595.
8. P. CALAMAI AND J. MORÉ, Projected gradient methods for linearly constrained problems, Math. Programming, Ser. B, 39 (1987), pp. 93-116.
9. R. CARTER, Fast Numerical Determination of Symmetric Sparsity Patterns, Tech. report MCS-P326-0992, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1992.
10. T. COLEMAN AND L. HULBERT, A direct active set algorithm for large sparse quadratic programs with simple bounds, Math. Programming, Ser. B, 20 (1983), pp. 187-209.
11. T. COLEMAN AND J. MORÉ, Estimation of sparse Jacobians matrices and graph coloring problems, SIAM J. Numer. Anal., 10 (1984), pp. 346-347.
12. A. CONN, N. GOULD, AND P. TOINT, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM J. Numer. Anal., 25 (1988), pp. 433-460.
13. A. CONN, N. GOULD, AND P. TOINT, Testing a class of methods for solving minimization problems with simple bounds on the variables, Math. Comp., 50 (1988), pp. 399-430.
14. A. CONN, N. GOULD, AND P. TOINT, LANCELOT-A Fortran Package for Large-Scale Nonlinear Optimization, Springer-Verlag, Berlin, New York, 1992.
15. R. COTTLE AND M. GOHEEN, A special class of large quadratic programs, in Nonlinear Programming 3, R. M. Meyer, O. Mangasarian, and S. Robinson, eds., Academic Press, New York, 1978, pp. 361-390.
16. J. DANIEL, Stability of the solution of definite quadratic programs, Math. Programming, 5 (1973), pp. 41-53.
17. G. DI PILLO, F. FACCHINEI, AND L. GRIPPO, An RQP algorithm using a differentiable exact penalty function for inequality constrained problems, Math. Programming, 55 (1992), pp. 49-68.
18. G. DI PILLO AND L. GRIPPO, A class of continuously differentiable exact penalty function algorithms for nonlinear programming problems, in System Modelling and Optimization, P. Toft-Christensen, ed., Springer-Verlag, Berlin, 1984, pp. 246-256.
19. G. DI PILLO, L. GRIPPO, AND S. LUCIDI, Globally convergent exact penalty algorithms for constrained optimization, in System Modelling and Optimization, A. Prekopa, J. Szelezsan, and B. Strazicky, eds., Springer-Verlag, Berlin, 1986, pp. 694-703.
20. I. DUFF, A. ERISMAN, AND J. REID, Direct Methods for Sparse Matrices, Clarendon Press, Oxford, 1986.
21. I. DUFF AND J. REID, The multifrontal solution of indefinite sparse symmetric linear equations, ACM Trans. Math. Software, 9 (1984), pp. 302-325.
22. J. DUNN, Global and asymptotic convergence rate estimates for a class of projected gradient process, SIAM J. Control Optim., 19 (1981), pp. 368-400.
23. 1 functions and the Maratos effect, Oper. Res. Lett., 17 (1995), pp. 131-137.
24. F. FACCHINEI AND S. LUCIDI, A Class of Penalty Functions for Optimization Problems with Bound Constraints. Part 2: Algorithms and Numerical Results, Tech. report 336, IASI-CNR, Roma, Italy, 1992.
25. F. FACCHINEI AND S. LUCIDI, Quadratically and superlinearly convergent algorithms for the solution of inequality constrained minimization problems, J. Optim. Theory Appl., 85 (1995), pp. 265-289.
26. P. GILL AND W. MURRAY. Newton-type methods for unconstrained and linearly constrained optimization, Math. Programming. 28 (1974), pp. 311-350.
27. P. GILL, W. MURRAY, AND M. WRIGHT, Practical Optimization, Academic Press, New York, 1981.
28. L. GRIPPO, F. LAMPARIELLO, AND S. LUCIDI, A class of nonmonotone stabilization methods in unconstrained optimization, Numer. Math., 59 (1991), pp. 779-805.
29. J. JÚDICE AND F. PIRES, A block principal pivoting algorithm for large-scale strictly monotone linear complementarity problems, Comput. Oper. Res., 21 (1994), pp. 587-596.
30. M. LESCRENIER, Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold, SIAM J. Numer. Anal., 28 (1991), pp. 476-495.
31. J. MORÉ AND G. TORALDO, Algorithms for bound constrained quadratic programming problems, Numer. Math., 55 (1989), pp. 377-400.
32. J. MORÉ AND G. TORALDO, Numerical solution of large quadratic programming problems with bound constraints, SIAM J. Control Optim., 1 (1991), pp. 93-113.
33. S. NASH AND A. SOFER, A barrier method for large-scale constrained optimization, ORSA J. Comput., 5 (1993), pp. 40-53.
34. J. ORTEGA AND W. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
35. M. POWELL AND P. TOINT, On the estimation of sparse hessian matrices, SIAM J. Numer. Anal., 16 (1979), pp. 1060-1074.
36. R. SCHNABEL AND E. ESKOW, A new modified Cholesky factorization, SIAM J. Sci. Statist. Comput., 11 (1990), pp. 1136-1158.
37. J. SOARES, Métodos de Newton para Optimizacao com Restrições Simples, Master's thesis, Departamento de Matemática, Universidade de Coimbra, Coimbra, Portugal, 1993.
38. J. SOARES, J. JÚDICE, AND F. FACCHINEI, An Active Set Newton's Methods for Large-Scale Nonlinear Programs with Box Constraints, Tech. report 367, IASI-CNR, Roma, Italy, 1993.