Modified Wilson's method for nonlinear programs with nonunique multipliers

Mathematics of Operations Research

Volumn 24, Issue 3, 1999, Pages 699-727

  Fischer, Andreas ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; NONLINEAR PROGRAMMING; PERTURBATION TECHNIQUES; PROBLEM SOLVING; VECTORS;

MODIFIED WILSON METHOD; MULTIPLIER VECTORS; NEWTON-TYPE METHODS;

OPERATIONS RESEARCH;

EID: 0033362367     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.24.3.699     Document Type: Article

References (29)

1. Bonnans, J. F. 1989. Local study of Newton-type algorithms for constrained problems. S. Dolecki, ed. Lecture Notes in Mathematics 1405, Springer, Berlin. 13-24.
2. _. 1994. Local analysis of Newton-type methods for variational inequalities and nonlinear programming. Appl. Math. Optim. 29 161-186.
3. Facchinei, F., A. Fischer, C. Kanzow. 1998a. Regularity properties of a new equation reformulation of variational inequalities. SIAM J. Optim. 8 850-869.
4. _, _, _. 1998b. On the accurate identification of active constraints. SIAM J. Optim. 9 14-32.
5. _, S. Lucidi. 1995. Quadratically and superlinearly convergent algorithms for the solution of inequality constrained minimization problems. J. Optim. Theory Appl. 85 265-289.
6. Fischer, A. 1992. A special Newton-type optimization method. Optimization 24 269-284.
7. Hager, W. W. 1997. Stabilized sequential quadratic programming. Technical Report, Department of Mathematics, University of Florida, Gainesville (revised 1998).
8. _, M. S. Gowda. 1997. Stability in the presence of degeneracy and error estimation. Technical Report, Department of Mathematics, University of Florida, Gainesville (revised 1997).
9. 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.
10. Janin, R. 1984. Directional derivative of the marginal function in nonlinear programming. Math. Programming Stud. 21 110-126.
11. Josephy, N. H. 1979. Newton's method for generalized equations. Technical Summary Report No 1965, Mathematical Research Center, University of Wisconsin-Madison.
12. Levitin, E. S., B. T. Polyak. 1966. Constrained minimization methods. Zh. Vychisl. Mat. i Mat. Fiz. 6 787-823. Translated in: Comput. Math. Math. Phys. 6 1-50.
13. Levitin, E. S., B. T. Polyak. 1966. Constrained minimization methods. Zh. Vychisl. Mat. i Mat. Fiz. 6 787-823. Translated in: Comput. Math. Math. Phys. 6 1-50.
14. Panier, E. R., A. L. Tits. 1993. On combining feasibility, descent and superlinear convergence in inequality constrained optimization. Math. Programming 59 261-276.
15. Pang, J.-S. 1993. Convergence of splitting and Newton methods for complementarity problems: An application of some sensitivity results. Math. Programming 58 149-160.
16. Pshenitchny, B. N. 1970. Newton's method for the solution of a system of equations and inequalities. Mat. Zametki 8 635-640.
17. _, Ju. M. Danilin. 1982. Numerische Methoden für Extremalaufgaben. Deutscher Verlag der Wissenschaften, Berlin.
18. Qi, L., Z. Wei. 1997. On the constant positive linear dependence condition and its application to an SQP method. Technical Report, School of Mathematics, The University of New South Wales, Sydney (revised 1998).
19. Ralph, D., S. J. Wright. 1997. Superlinear convergence of an interior-point method for monotone variational inequalities. M. C. Ferris, J.-S. Pang, eds. Complementarity and Variational Problems: State of the Art. SIAM, Philadelphia. 345-385.
20. _, _. 1996. Superlinear convergence of an interior-point method despite dependent constraints. Preprint MCS-P622-1196, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne.
21. Robinson, S. M. 1972. Extension of Newton's method to nonlinear functions with values in a cone. Numer. Math. 19 341-347.
22. _. 1974. Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear programming algorithms. Math. Programming 7 1-16.
23. _. 1980. Strongly regular generalized equations. Math. Oper. Res. 5 43-62.
24. _. 1981. Some continuity properties of polyhedral multifunctions. Math. Programming Stud. 14 206-214.
25. _. 1982. Generalized equations and their solutions, Part II: Applications to nonlinear programming. Math. Programming Stud. 19 200-221.
26. Vetters, K. 1970. Quadratische Approximationsmethoden zur konvexen Optimierung. Z. Angew. Math. Mech. 50 479-484.
27. Wilson, R. B. 1963. A simplicial algorithm for concave programming. Ph.D. thesis, Graduate School of Business Administration, Harvard University, Cambridge, MA.
28. Wright, S. J. 1998. Superlinear convergence of a stabilized SQP method to a degenerate solution. Comput. Optim. Appl. 11 253-275.
29. _. 1997. Modifying SQP for degenerate problems. Preprint MCS-P699-1097, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne.