Disjunctive optimization: Critical point theory

Journal of Optimization Theory and Applications

Volumn 93, Issue 2, 1997, Pages 321-336

  Jongen, H T ^a   Ruckmann J J ^a   Stein, O ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b UNIVERSITY OF TRIER   (Germany)

Author keywords

Deformations; Disjunctive optimization; Morse theory; Stationary index; Stationary points

Indexed keywords

CONSTRAINT THEORY; OPTIMIZATION; TOPOLOGY;

CELL ATTACHMENTS; CRITICAL POINTS THEORY; DISJUNCTIVE OPTIMIZATION; MORSE THE-ORY; NONDEGENERATE; OPTIMISATIONS; OPTIMIZATION PROBLEMS; POINT SET; STATIONARY INDEX; STATIONARY POINTS;

DEFORMATION;

EID: 0040055948     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022650006477     Document Type: Article

References (14)

1. BALAS, E., Disjunctive Programming, Annals of Discrete Mathematics, Vol. 5, pp. 3-51, 1979.
2. HETTICH, R., and STILL, G., Semi-Infinite Programming Models in Robotics, Parametric Optimization and Related Topics II, Edited by J. Guddat et al., Mathematical Research, Akademie Verlag, Berlin, Germany, Vol. 62, pp. 112-118, 1991.
3. MILNOR, J., Morse Theory, Annals of Mathematics Studies, Princeton University Press, Princeton, New Jersey, Vol. 51, pp. 1-153, 1963.
4. n, I: Morse Theory, Chebyshev Approximation, Peter Lang Verlag, Frankfurt/Main, Germany, 1983.
5. GUDDAT, J., JONGEN, H. T., and RÜCKMANN, J.-J., On Stability and Stationary Points in Nonlinear Optimization, Journal of the Australian Mathematical Society, Vol. 28B, pp. 36-56, 1986.
6. SPANIER, E. H., Algebraic Topology, McGraw-Hill, New York, New York, 1966.
7. HELBIG, S., Duality in Disjunctive Programming via Vector Optimization, Mathematical Programming, Vol. 65, pp. 21-41, 1994.
8. BARTELS, S. G., KUNTZ, L., and SCHOLTES, S., Continuous Selections of Linear Functions and Nonsmooth Critical Point Theory, Nonlinear Analysis, Theory, Methods, and Applications, Vol. 24, pp. 385-407, 1995.
9. JONGEN, H. T., and PALLASCHKE, D., On Linearization and Continuous Selections of Functions, Optimization, Vol. 19, pp. 343-353, 1988.
10. FIACCO, A. V., and MCCORMICK, G. P., Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Wiley, Chichester, England, 1968.
11. JONGEN, H. T., TWILT, F., and WEBER, G.-W., Semi-Infinite Optimization: Structure and Stability of the Feasible Set, Journal of Optimization Theory and Applications, Vol. 72, pp. 529-552, 1992.
12. RÜCKMANN, J.-J., Stability of Noncompact Feasible Sets in Nonlinear Optimization, Parametric Optimization and Related Topics III, Edited by J. Guddat et al., Peter Lang Verlag, Frankfurt/Main, Germany, pp. 467-502, 1993.
13. HIRSCH, M. W., Differential Topology, Springer Verlag, Berlin, Germany, 1976.
14. PALAIS, R. S., and SMALE, S., A Generalized Morse Theory, Bulletin of the American Mathematical Society, Vol. 70, pp. 165-172, 1964.