Discretization in semi-infinite programming: The rate of convergence

Mathematical Programming, Series B

Volumn 91, Issue 1, 2001, Pages 53-69

  Still, G ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Discretization methods; Rate of convergence; Semi infinite programming

Indexed keywords

EID: 0347709479     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070100239     Document Type: Article

References (20)

1. Cheney, E.W. (1982): Introduction to approximation theory. Chelsea, New York, 2nd edition
2. Dunham, C.B. (1974): Efficiency of Chebyshev approximation on finite subsets. J. Assoc. Comp. Mach. 21, 2, 311-313
3. Dunham, C.B., Williams, J. (1981): Rate of convergence of discretization in Chebyshev approximation. Math. Comput. 37, 155, 135-139
4. Gramlich, G., Hettich, R., Sachs, E.W. (1995): Local convergence of SQP-methods in semi-infinite programming. SIAM J. Optim. 5, 3, 641-658
5. Hettich, R., Zencke, P. (1982): Numerische Methoden der Approximation und semi-infiniten Optimierung. Teubner, Stuttgart
6. Hettich, R. (1986): An implementation of a discretization method for semi-infinite programming. Math. Program. 34, 354-361
7. Hettich, R., Gramlich, G. (1990): A note on an implementation of a method for quadratic semi-infinite programming. Math. Program. 46, 249-254
8. Hettich, R., Kortanek, K. (1993): Semi-infinite programming: Theory, methods and applications. SIAM Rev. 35, 3, 380-429
9. Hettich, R., Still, G. (1995): Second order optimality conditions for generalized semi-infinite programming problems. Optimization 34, 195-211
10. Lawrence, C.T., Tits, A.L. (1998): Feasible sequential quadratic programming for finely discretized problems for SIP. In: 'Semi-infinite Programming', Reemtsen/Ruckmann (eds.), Kluwer, Boston, pp. 159-193
11. Opfer, G. (1982): Solving complex approximation problems by semi-infinite optimization techniques: A study on convergence. Numer. Math. 39, 411-420
12. Panier, E.R., Tits, A.L. (1989): A globally convergent algorithm with adaptively refined discretization for semi-infinite optimization problems arising in engineering design. IEEE Trans. Automat. Contr. AC-34, 903-908
13. Polak, E. (1997): Optimization, Algorithms and consistent Approximations. Springer, Berlin
14. Reemtsen, R. (1994): Some outer approximation methods for semi-infinite optimization problems. J. Comp. Appl. Math. 53, 87-108
15. Reemtsen, R., Görner, S. (1998): Numerical methods for semi-infinite programming: A survey. In: 'Semi-infinite Programming', Reemtsen/Rückmann (eds.), Kluwer, Boston, pp. 195-262
16. Rückmann, J.-J., Stein, O.: On linear and linearized generalized semi-infinite problems. Ann. Oper. Res. (to appear)
17. Still, G. (1997): Vector-valued approximation problems; Numerical and genericity aspects. Proceedings of the 3rd International Conference on Approximation and Optimization (Puebla 1995), (16pp. electronic), Benemerita Univ. Auton. Puebla, Puebla
18. Still, G. (1999): Generalized semi-infinite programming: Theory and methods. Eur. J. Oper. Res. 119, 301-313
19. Still, G. (2001): Generalized semi-infinite programming: Numerical aspects. Optimization 49, 223-242
20. Tanaka, Y. (1999): A trust region method for semi-infinite programming problems. Intern. J. Systems Sci. 30, 199-204