An algorithm for degenerate nonlinear programming with rapid local convergence

SIAM Journal on Optimization

Volumn 15, Issue 3, 2005, Pages 673-696

  Wright, Stephen J ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

Degeneracy; Nonlinear programming; Superlinear convergence

Indexed keywords

DEGENERACY; MODELING LANGUAGES; PRIMAL-DUAL SOLUTION; SUPERLINEAR CONVERGENCE;

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; LINEAR SYSTEMS; OPTIMIZATION; PERTURBATION TECHNIQUES; QUADRATIC PROGRAMMING; SET THEORY;

NONLINEAR PROGRAMMING;

EID: 23844554186     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/030601235     Document Type: Article

References (17)

1. M. ANITESCU, Degenerate nonlinear programming with a quadratic growth condition, SIAM J. Optim., 10 (2000), pp. 1116-1135.
2. D. P. BERTSEKAS, Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, 1982.
3. J. F. BONNANS AND A. IOFFE, Second-order sufficiency and quadratic growth for nonisolated minima, Math. Oper. Res., 20 (1995), pp. 801-819.
4. F. FACCHINEI, A. FISCHER, AND C. KANZOW, On the accurate identification of active constraints, SIAM J. Optim., 9 (1998), pp. 14-32.
5. A. FISCHER, Modified Wilson method for nonlinear programs with nonunique multipliers, Math. Oper. Res., 24 (1999), pp. 699-727.
6. A. FISCHER, Local behavior of an iterative framework for generalized equations with nonisolated solutions, Math. Program. Ser. A, 94 (2002), pp. 91-124.
7. R. FLETCHER, S. LEYFFER, D. RALPH, AND S. SCHOLTES, Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints, Numerical Analysis Report NA/209, Department of Mathematics, University of Dundee, May 2002.
8. W. W. HAGER, Stabilized sequential quadratic programming, Comput. Optim. Appl., 12 (1999), pp. 253-273.
9. W. W. HAGER AND M. S. GOWDA, Stability in the presence of degeneracy and error estimation, Math. Program. Ser. A, 85 (1999), pp. 181-192.
10. M. R. HESTENES, Multiplier and gradient methods, J. Optim. Theory Appl., 4 (1969), pp. 303-320.
11. A. F. IZMAILOV AND M. V. SOLODOV, Newton-type methods for optimization problems without constraint qualifications, SIAM J. Optim., 15 (2004), pp. 210-228.
12. J. NOCEDAL AND S. J. WRIGHT, Numerical Optimization, Springer, New York, 1999.
13. M. J. D. POWELL, A method for nonlinear constraints in minimization problems, in Optimization, R. Fletcher, ed., Academic Press, New York, 1969, pp. 283-298.
14. S. M. ROBINSON, Generalized equations and their solutions. Part II: Applications to nonlinear programming, Math. Program. Stud., 19 (1982), pp. 200-221.
15. S. J. WRIGHT, Superlinear convergence of a stabilized SQP method to a degenerate solution, Comput. Optim. Appl., 11 (1998), pp. 253-275.
16. S. J. WRIGHT, Modifying SQP for degenerate problems, SIAM J. Optim., 13 (2002), pp. 470-497.
17. S. J. WRIGHT, Constraint identification and algorithm stabilization for degenerate nonlinear programs, Math. Program. Ser. B, 95 (2003), pp. 137-160.