On the analytical and numerical stability of critical lagrange multipliers

Computational Mathematics and Mathematical Physics

Volumn 45, Issue 6, 2005, Pages 930-946

  Izmailov, A F ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Constrained optimization problems; Lagrange multipliers; Stability of critical Lagrange multipliers

Indexed keywords

EID: 33746532551     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. S. M. Robinson, "Variational Conditions with Smooth Constraints: Structure and Analysis," Math. Program. 97 (1-2), 245-265 (2003).
2. S. M. Robinson, "Strongly Regular Generalized Equations," Math. Operat. Res. 5, 43-62 (1980).
3. A. F. Izmailov and A. A. Tret'yakov, 2-Regular Solutions of Nonlinear Problems: Theory and Numerical Methods (Fizmatlit, Moscow, 1999) [in Russian].
4. E. R. Avakov, "Theorems about Estimates in the Neighborhood of a Singular Point of a Mapping," Mat. Zametki 47 (5), 3-13 (1990).
5. A. F. Izmailov, "Theorems on Representation of Families of Nonlinear Mappings and Implicit Function Theorems," Mat. Zametki 67 (1), 57-68 (2000).
6. A. V. Arutyunov, "Implicit Function Theorem as an Implementation of Lagrange's Priciple: Abnormal Points," Mat. Sb. 191 (1), 3-26 (2000).
7. A. V. Arutyunov and A. F. Izmailov, "Sensitivity Theory for Abnormal Optimization Problems with Equality Constraints," Zh. Vychisl. Mat. Mat. Fiz. 43, 186-202 (2003)
8. [Comput. Math. Math. Phys. 43, 178-193 (2003)].
9. A. F. Izmailov, "Higher Order Necessary Conditions in Optimization Problems," Zh. Vychisl. Mat. Mat. Fiz. 32, 1310-1313 (1992).
10. A. F. Izmailov and A. A. Tret'yakov, Factor Analysis of Nonlinear Mappings (Nauka, Moscow, 1994) [in Russian].
11. A. F. Izmailov and M. V. Solodov, "Newton-Type Methods for Optimization Problems without Constraint Qualifications," SIAM J. Optim. 15 (1), 210-228 (2004).
12. W. W. Hager and M. S. Gowda, "Stability in the Presence of Degeneracy and Error Estimation," Math. Program. 85, 181-192 (1999).
13. A. F. Izmailov and M. V. Solodov, Numerical Optimization Methods (Fizmatlit, Moscow, 2003) [in Russian].
14. A. Fischer, "Local Behavior of an Iterative Framework for Generalized Equations with Nonisolated Solutions," Math. Program. 94, 91-124 (2002).
15. S. J. Wright, "Modifying SQP for Degenerate Problems," SIAM J. Optim. 13, 470-497 (2002).
16. O. A. Brezhneva and A. F. Izmailov, "Construction of Defining Systems for Finding Singular Solutions to Nonlinear Equations," Zh. Vychisl. Mat. Mat. Fiz. 42, 10-22 (2002)
17. [Comput. Math. Math. Phys. 42, 8-19 (2002)].
18. T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, Berlin, 1966; Mir, Moscow, 1972).