A note on error estimates for some interior penalty methods

Lecture Notes in Economics and Mathematical Systems

Volumn 563, Issue , 2006, Pages 133-146

  Izmailov, Alexey F ^a   Solodov, Mikhail V ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b IMPA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 53349118612     PISSN: 00758442     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-28258-0_9     Document Type: Conference Paper

References (14)

1. L. Bittner. Eine Verallgemeinerung des Verfahrens des logarithmischen Potentials von Frisch für nichtlineare Optimierungprobleme. In: A. Pekora (ed.), Colloquium on Applications of Mathematics to Economics, Budapest, 1963, Akademiai Kiado. Publishing House of the Hungarian Acad, of Sciences, 1965.
2. J.F. Bonnans and A. Shapiro. Perturbation Analysis of Optimization Problems. Springer-Verlag, New York, 2000.
3. A.V. Fiacco and G.P. McCormick. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. John Wiley & Sons, New York, 1968.
4. A. Fischer. Local behaviour of an iterative framework for generalized equations with nonisolated solutions. Math. Program. 94: 91-124, 2002.
5. C. Grossman, D. Klatte, and B. Kummer. Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ. Kybernetika 40: 571-584, 2004.
6. W.W. Hager and M.S. Gowda. Stability in the presence of degeneracy and error estimation. Math. Program. 85: 181-192, 1999.
7. A.F. Izmailov and M.V. Solodov. Computable primal error bounds based on the augmented Lagrangian and Lagrangian relaxation algorithms. Preprint A 2004/303, IMPA, Rio de Janeiro, 2004.
8. A.F. Izmailov and M.V. Solodov. Karush-Kuhn-Tucker systems: regularity conditions, error bounds and a class of Newton-type methods. Math. Program. 95: 631-650, 2003.
9. O.L. Mangasarian. Nonlinear Programming McGraw-Hill, New York, 1969
10. R. Mifflin. On the convergence of the logarithmic barrier function method. In: F.A. Lootsma (ed.), Numerical Methods for Nonlinear Optimization. Academic Press, London, 1972.
11. R. Mifflin. Convergence bounds for nonlinear programming algorithms. Math. Program. 8: 251-271, 1975.
12. J.S. Pang. Error bounds in mathematical programming. Math. Program. 79: 299-332, 1997.
13. S.M. Robinson. Stability theorems for systems of inequalities, Part II: differentiable nonlinear systems. SIAM J. Numer. Anal. 13: 497-513, 1976.
14. S.J. Wright and D. Orban. Properties of the log-barrier function on degenerate nonlinear programs. Math. Oper. Res. 27: 585-613, 2002.