Approximate efficiency and scalar stationarity in unbounded nonsmooth convex vector optimization problems

Journal of Optimization Theory and Applications

Volumn 106, Issue 2, 2000, Pages 265-296

  Bolintineanu S ^a  

^a UNIVERSITÉ DE PERPIGNAN   (France)

Author keywords

Convex analysis; Kuhn Tucker sequences; Minimizing sequences; Multicriteria optimization; Pareto optimizing sequences; Stationary sequences; Vector optimization; Weakly efficient sequences; Weakly infimal sets

Indexed keywords

FUNCTIONS; PARETO PRINCIPLE; VECTOR SPACES; VECTORS;

CONVEX ANALYSIS; INFIMAL SET; KUHN-TUCK SEQUENCE; KUHN-TUCKER; MINIMIZING SEQUENCE; MULTI-CRITERIA OPTIMISATION; PARETO OPTIMIZING SEQUENCE; STATIONARY SEQUENCE; VECTOR OPTIMIZATIONS; WEAKLY-EFFICIENT SEQUENCE; WEAKLY-INFIMAL SET;

MULTIOBJECTIVE OPTIMIZATION;

EID: 0034347944     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004695229456     Document Type: Article

References (24)

1. 1. AUSLENDER, A., and CROUZEIX, J. P., Well-Behaved Asymptotical Convex Functions, Analyse Non Linéaire, Gauthier-Villars, Paris, France, pp. 101-122, 1989.
2. 2. ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
3. 3. AUSLENDER, A., COMINETTI, R., and CROUZEIX, P., Functions with Unbounded Level Sets and Applications to Duality Theory, SIAM Journal on Optimization, Vol. 3, pp. 669-687, 1993.
4. 4. AUSLENDER, A., How to Deal with the Unbounded in Optimization: Theory and Algorithms, Mathematical Programming, Vol. 79, pp. 3-18, 1997.
5. 5. CHOU, C. C., NG, K. F., and PANG, J. S., Minimizing and Stationary Sequences of Optimization Problems, SIAM Journal on Control and Optimization, Vol. 6, pp. 1908-1936, 1998.
6. 6. PANG, J. S., Error Bounds in Mathematical Programming, Mathematical Programming, Vol. 79, pp. 229-332, 1997.
7. 7. BERNOUSSI, B., BOLINTINÉANU, S., and CHOU, C. C., Pareto Optimizing and Scalarly Stationary Sequences, Journal of Mathematical Analysis and Applications, Vol. 220, pp. 553-561, 1998.
8. 8. SAWARAGI, Y., NAKAYAMA, H., and TANINO, T., Theory of Multiobjective Optimization, Academic Press, Orlando, Florida, 1985.
9. 9. BERNOUSSI, B., BOLINTINÉANU, S., CHOU, C. C., and EL MAGHRI, M., Efficient and Kuhn-Tucker Sequences in Constrained Vector Optimization Problems, International Symposium on Mathematical Programming, Lausanne, Switzerland, 1997.
10. 10. ATTOUCH, H., and RIAHI, R., Stability Results for Ekeland's ∈-Variational Principle and Cone Extremal Solutions, Mathematics of Operation Research, Vol. 18, pp. 173-201, 1993.
11. 11. LEMAIRE, B., Approximation in Multiobjective Optimization, Journal of Global Optimization, Vol. 2, pp. 117-312, 1992.
12. 12. LORIDAN, P., ∈-Solutions in Vector Minimization Problems, Journal of Optimization Theory and Applications, Vol. 43, pp. 265-276, 1984.
13. 13. LORIDAN, P., Well-Posedness in Vector Optimization, Recent Developments in Well-Posed Variational Problems, Edited by R. Lucchetti and J. Revalski, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 171-192, 1995.
14. 14. PENOT, J. P., and STERNA-KARWAT, A., Parametrized Multicriteria Optimization: Continuity and Closedness of Optimal Multifunctions, Journal of Mathematical Analysis and Applications, Vol. 120, pp. 150-168, 1986.
15. 15. DOLECKI, S., and MALIVERT, C., Polarities and Stability in Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, Vol. 294, pp. 96-113, 1987.
16. 16. PENOT, J. P., Compact Nets, Filters, and Relations, Journal of Mathematical Analysis and Applications, Vol. 93, pp. 400-417, 1983.
17. 17. BORWEIN, J. M., PENOT, J. P., and THERA, M., Conjugate Convex Operators, Journal of Mathematical Analysis and Applications, Vol. 102, pp. 399-414, 1984.
18. 18. BOLINTINÉANU, S., Vector Variational Principles, ∈-Efficiency, and Scalar Stationarity, Journal of Convex Analysis (to appear).
19. 19. LUC, D. T., Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 319, 1989.
20. 20. CLARKE, F. H., Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, NY, 1983.
21. 21. IOFFE, A. D., and TIHOMIROV, V. M., Theory of Extremal Problems, North-Holland, Amsterdam, Netherlands, 1979.
22. 22. DAUER, J. P., and STADLER, W., A Survey of Vector Optimization in Infinite - Dimensional Spaces, Part 2, Journal of Optimization Theory and Applications, Vol. 51, pp. 205-241, 1986.
23. 23. AUBIN, J. P., and EKELAND, I., Applied Nonlinear Analysis, John Wiley and Sons, New York, NY, 1984.
24. 24. Yu, P. L., Multiple-Criteria Decision Making, Plenum Press, New York, NY, 1985.