Fenchel-Lagrange duality versus geometric duality in convex optimization

Journal of Optimization Theory and Applications

Volumn 129, Issue 1, 2006, Pages 33-54

  Bot R I ^a   Grad, S M ^a   Wanka, G ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Conjugate functions; Convex optimization; Geometric programming; Lagrange and Fenchel duality; Perturbation theory

Indexed keywords

GEOMETRY; LAGRANGE MULTIPLIERS; PERTURBATION TECHNIQUES;

CONDITION; CONJUGATE FUNCTIONS; CONVEX OPTIMISATION; FENCHEL DUALITY; GEOMETRIC DUALITY; GEOMETRIC PROGRAMMING; LAGRANGE DUALITY; OPTIMALITY CONDITIONS; PERTURBATION THEORY; STRONG DUALITY;

CONVEX OPTIMIZATION;

EID: 30944462375     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-006-9047-2     Document Type: Article

References (24)

1. SCOTT, C. H., and JEFFERSON, T. R., Avenues of Geometric Programming, I: Theory, New Zealand Operational Research, Vol. 6, pp. 109-136, 1978.
2. SCOTT, C. H., and JEFFERSON, T. R., On Duality for a Class of Quasiconcave Multiplicative Programs, Journal of Optimization Theory and Applications, Vol. 117, pp. 575-583, 2003.
3. PETERSON, E. L., Geometric Programming, SIAM Review, Vol. 18, pp. 1-51, 1976.
4. JEFFERSON, T. R., and SCOTT, C. H., Quadratic Geometric Programming with Application to Machining Economics, Mathematical Programming, Vol. 31, pp. 137-152, 1985.
5. JEFFERSON, T. R., and SCOTT, C. H., Quality Tolerancing and Conjugate Duality, Annals of Operations Research, Vol. 105, pp. 185-200, 2001.
6. JEFFERSON, T. R., WANG, Y. P., and SCOTT, C. H., Composite Geometric Programming, Journal of Optimization Theory and Applications, Vol. 64, pp. 101-118, 1990.
7. SCOTT, C. H., and JEFFERSON, T. R., Avenues of Geometric Programming, II: Applications, New Zealand Operational Research, Vol. 7, pp. 51-68, 1979.
8. SCOTT, C. H., and JEFFERSON, T. R., Conjugate Duality in Generalized Fractional Programming, Journal of Optimization Theory and Applications, Vol. 60, pp. 475-483, 1989.
9. SCOTT, C. H., and JEFFERSON, T. R., Convex Dual for Quadratic. Concave Fractional Programs, Journal of Optimization Theory and Applications, Vol. 91, pp. 115-122, 1996.
10. SCOTT, C. H., and JEFFERSON, T. R., Duality for a Sum of Convex Ratios, Optimization, Vol. 40, pp. 303-312, 1997.
11. SCOTT, C. H., and JEFFERSON, T. R., Duality for Minmax Programs, Journal of Mathematical Analysis and Applications, Vol. 100, pp. 385-393, 1984.
12. SCOTT, C.H., JEFFERSON, T.R., and JORJANI, S., Conjugate Duality in Facility Location, Facility Location: A Survey of Applications and Methods, Edited by Z. Drezner, Springer Verlag, Heidelberg, Germany, pp. 89-101, 1995.
13. SCOTT, C. H., JEFFERSON, T. R., and JORJANI, S., Duality for Programs Involving Nonseparable Objective Functions, International Journal of Systems Science, Vol. 19, pp. 1911-1918, 1988.
14. SCOTT, C. H., JEFFERSON, T. R., and JORJANI, S., On Duality for Entropy-Constrained Programs, Information Sciences, Vol. 35, pp. 211-221, 1985.
15. BOŢ, R. I., GRAD, S. M., and WANKA, G., Entropy-Constrained Programs and Geometric Duality Obtained via Fenchel-Lagrange Duality Approach, Nonlinear Analysis Forum, Vol. 9, pp. 65-85, 2004.
16. EKELAND, I., and TEMAM, R., Convex Analysis and Variational Problems, North-Holland Publishing Company, Amsterdam, Netherlands, 1976.
17. ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
18. BOT, R. I., KASSAY, G., and WANKA, G., Strong Duality for Generalized Convex Optimization Problems, Journal of Optimization Theory and Applications, Vol. 127, pp. 45-70, 2005.
19. WANKA, G., and BOŢ, R. I., New Duality Approach for Multiobjective Convex Optimization Problems, Journal of Nonlinear and Convex Analysis, Vol. 3, pp. 41-57, 2002.
20. WANKA, G., and BOŢ, R. I., Multiobjective Duality for Convex-Linear Problems, II, Mathematical Methods of Operations Research, Vol. 53, pp. 419-433, 2001.
21. WANKA, G., and BOŢ, R. I., Multiobjective Duality for Convex Ratios, Journal of Mathematical Analysis and Applications, Vol. 275, pp. 354-368, 2002.
22. WANKA, G., and BOT, R. I., On the Relations between Different Dual Problems in Convex Mathematical Programming, Operations Research Proceedings 2001, Edited by P. Chamoni, R. Leisten, A. Martin, J. Minnemann, and H. Stadtler, Springer Verlag, Heidelberg, Germany, pp. 255-262, 2002.
23. DUFFIN, R. J., PETERSON, E. L., and ZENER, C., Geometric Programming: Theory and Applications, John Wiley and Sons, New York, NY, 1967.
24. ELSTER, K. H., REINHARDT, R., SCHÄUBLE, M., and DONATH, G., Einführung in die nichtlineare Optimierung, Mathematisch - Naturwissenschaftliche Bibliothek, BSB B.G. Teubner Verlagsgesellschaft, Leipzig, Germany, 1977.