One-Parameter Families of Feasible Sets in Semi-infinite Optimization

Journal of Global Optimization

Volumn 14, Issue 2, 1999, Pages 181-204

  Jongen, H Th ^a   Ruckmann J J ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Bifurcation point; Feasible set; Mangasarian Fromovitz constraint qualification; Parametric family; Semi infinite optimization

Indexed keywords

EID: 0005245304     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008282216306     Document Type: Article

References (18)

1. Berge, C. (1963), Topological Spaces. Oliver and Boyd, Edinburgh, London.
2. Fiacco, A.V. (1983), Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York.
3. Guddat, J., Jongen, H.Th. and Rückmann, J.-J. (1986), On stability and stationary points in nonlinear optimization, J. Austral. Math. Soc., Ser. B 28: 36-56.
4. Hettich, R., Jongen, H.Th. and Stein, O. (1995), On continuous deformations of semi-infinite optimization problems, in M. Florenzano et al. (eds.), Approximation and Optimization in the Carribean II (Peter Lang, Frankfurt), pp. 406-424.
5. Hettich, R. and Kortanek, K.O. (1993), Semi-infinite programming: theory, methods and applications, SIAM Rev. 35(3): 380-429.
6. Hettich, R. and Zencke, P. (1982), Numerische Methoden der Approximation und semi-infiniten Optimierung. Teubner, Stuttgart.
7. Hirsch, M.W. (1976), Differential Topology. Springer, Berlin, Heidelberg, New York.
8. Jiménez, M.A. and Rückmann, J.-J. (1995), On equivalent stability properties in semi-infinite optimization, Z. Oper. Res. 41(2): 175-190.
9. Jongen, H.Th., Jonker, P. and Twilt, F. (1982), On one-parameter families of sets defined by (in)equality constraints, Nieuw Archief voor Wiskunde 30(3): 307-322.
10. n, I. Morse Theory, Chebyshev Approximation. Peter Lang, Frankfurt.
11. n, II. Transversality, Flows, Parametric Aspects. Peter Lang, Frankfurt.
12. Jongen, H.Th., Rückmann, J.-J. and Weber, G.-W (1994), One-parametric semi-infinite optimization: on the stability of the feasible set, SIAM J. Opt. 4(3): 637-648.
13. Jongen, H.Th. and Stein, O. (1997), On generic one-parametric semi-infinite optimization, SIAM J. Opt. 7(4): 1103-1137.
14. Jongen, H.Th., Twilt, F. and Weber, G.-W. (1992), Semi-infinite optimization: structure and stability of the feasible set, J. Optim. Theory Appl. 72: 529-552.
15. Polak, E. (1987), On the mathematical foundations of nondifferentiable optimization in engineering design, SIAM Rev. 29: 21-89.
16. Reemtsen, R. and Rückmann, J-J. (eds.) (1998), Semi-infinite Programming. Kluwer Academic Publishers, Dordrecht / Boston / London.
17. Rupp, T. (1989), Kuhn-Tucker curves for one-parametric semi-infinite programming, Optimization, 20: 61-77.
18. Spanier, E.H. (1966), Algebraic Topology. McGraw Hill, New York.