Superlinear convergence of an interior-point method despite dependent constraints

Mathematics of Operations Research

Volumn 25, Issue 2, 2000, Pages 179-194

  Ralph, Daniel ^a   Wright, Stephen J ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; MATRIX ALGEBRA; VARIATIONAL TECHNIQUES;

CONSTANT RANK CONDITIONS; SUPERLINEAR CONVERGENCE;

OPERATIONS RESEARCH;

EID: 0034187335     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.25.2.179.12227     Document Type: Article

References (15)

1. Bonnans, J. F. 1989. Local study of newton type algorithms for constrained problems. S. Dolecki, ed. Optimization-Fifth French-German Conference. Number 1405, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Germany. 13-24.
2. Facchinei, F., A. Fischer, C. Kanzow. 1998. On the accurate identification of active constraints. SIAM J Optim, 9 (1) 14-32.
3. Fischer, A. 1997, February. Modified Wilson's method for nonlinear programs with nonunique multipliers. Math. Oper. Res. 24 699-727.
4. Hager, W. W. 1999. Stabilized sequential quadratic programming. Comput. Optim. Appl 12 253-273.
5. Harker, P. T., J.-S. Pang. 1990. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Math. Programming 48 161-220.
6. Monterio, R. D. C., S. J. Wright. 1994. Local convergence of interior-point algorithms for degenerate monotone LCP. Comput. Optim. Appl. 3 131-155.
7. _, F. Zhou. 1997. On superlinear convergence of infeasible-interior-point algorithms for linear constrained convex programs. Comput. Optim. Appl. 8 245-262.
8. Pang, J.-S. 1993. Convergence of splitting and Newton methods for complementarity problems: An application of some sensitivity results. Math. Programming 58 149-160.
9. Qi, L., Z. Wei, 1997. On the constant positive linear independence and its application to SQP methods. Technical report, School of Mathematics, The University of New South Wales, Australia.
10. Ralph, D., S. J. Wright. 1997. Superlinear convergence of an interior-point method for monotone variational inequalities. In M. C. Ferris, J. Pang, eds. Complementarity and Variantional Problems: State of the Art, SIAM Publications, Philadelphia, PA. 345-385.
11. Wright, S. J. 1996. A path-following interior-point algorithm for linear and quadratic optimization problems. Ann. Oper. Res. 62 103-130.
12. _. 1997a, October. Modifying SQP for degenerate problems. Preprint ANL/MCS-P699-1097, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL.
13. _. 1997b. Primal-Dual Interior-Point Methods. SIAM Publications, Philadelphia, PA.
14. _. 1998a, January. Effects of finite-precision arithmetic on interior-point methods for nonlinear programming. Preprint ANL/MCS-P705-0198, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL.
15. _, 1998b. Superlinear convergence of a stabilized SQP method to a degenerate solution. Comput. Optim. Appl. 11 253-275.