On minima of the difference of functions

Journal of Optimization Theory and Applications

Volumn 93, Issue 3, 1997, Pages 525-531

  Flores Bazan F ^a  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

Author keywords

Generalized conjugation; Lower semicontinuity; Nonconvex functions; Phi subdifferentials

Indexed keywords

ARBITRARY FUNCTIONS; CONDITION; GENERALIZED CONJUGATION; LOWER SEMI-CONTINUOUS FUNCTIONS; LOWER SEMICONTINUITY; METRIC SPACES; NONCONVEX FUNCTIONS; PHI-SUBDIFFERENTIAL; SUBDIFFERENTIALS;

EID: 0031516423     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022686911986     Document Type: Article

References (17)

1. HIRIART-URRUTY, J. B., Generalized Differentiability, Duality, and Optimization for Problems Dealing with Differences of Convex Functions, Convexity and Duality in Optimization, Lecture Notes in Economics and Mathematical Systems, Edited by J. Ponstein, Springer Verlag, Berlin, Germany, Vol. 256, pp. 37-70, 1986.
2. HIRIART-URRUTY, J. B., From Convex Optimization to Nonconvex Optimization: Necessary and Sufficient Conditions for Global Optimality, Nonsmooth Optimization and Related Topics, Edited by F. H. Clarke, V. F. Demyanov, and F. Giannessi, Plenum, New York, New York, pp. 219-235, 1989.
3. MARTINEZ-LEGAZ, J. E., and SEEGER, A., A Formula on the Approximate Sub-differential of the Difference of Convex Functions, Bulletin of the Australian Mathematical Society, Vol. 45, pp. 37-41, 1992.
4. TOLAND, J. F., A Duality Principle for Nonconvex Optimization and the Calculus of Variations, Archive for Rational Mechanics and Analysis, Vol. 71, pp. 41-61, 1979.
5. TOLAND, J. F., Duality in Nonconvex Optimization, Journal of Mathematical Analysis and Applications, Vol. 66, pp. 399-415, 1978.
6. SINGER, I., A Fenchel-Rockafellar Type Duality Theorem for Maximization, Bulletin of the Australian Mathematical Society, Vol. 29, pp. 193-198, 1979.
7. SINGER, I., Maximization of Lower Semicontinuous Convex Functional on Bounded Subsets of Locally Convex Spaces, Part 2: Quasi-Lagrangian Duality Theorems, Resultateder Mathematik, Vol. 3, pp. 235-248, 1980.
8. HIRIART-URRUTY, J. B., A General Formula on the Conjugate of the Difference of Functions, Canadian Mathematical Bulletin, Vol. 29, pp. 482-485, 1986.
9. ELLAIA, R., and HIRIART-URRUTY, J. B., The Conjugate of the Difference of Convex Functions, Journal of Optimization Theory and Applications, Vol. 49, pp. 493-498, 1986.
10. TUY, H., and OETTLI, W., On Necessary and Sufficient Conditions for Global Optimally, Revista de Matemáticas Aplicadas, Vol. 15, pp. 39-41, 1993.
11. MOREAU, J. J., Inf-Convolution, Sous-Additivité, Convexité des Fonctions Numériques, Journal de Mathématiques Pures et Appliquées, Vol. 49, pp. 109-154, 1970.
12. MARTINEZ-LEGAZ, J. E., Generalized Conjugation and Related Topics, Generalized Convexity and Fractional Programming with Economic Applications, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 345, pp. 198-218, 1990.
13. SINGER, I., Generalizations of Convex Supremization Duality, Nonlinear Convex Analysis, Edited by B. L. Lin and S. Simons, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, New York, Vol. 109, pp. 253-270, 1987.
14. VOLLE, M., Contributions à la Dualité en Optimisation et à l'Épiconvergence, Thèse, Université de Pau, Pau, France, 1986.
15. FLORES-BAZÁN, F., On a Notion of Subdifferentiability for Nonconvex Functions, Optimization, Vol. 33, pp. 1-8, 1995.
16. FLORES-BAZÁN, F., The Lack of Lower Semicontinuity and Nonexistence of Minimizers, Nonlinear Analysis: Theory, Methods, and Applications, Vol. 23, pp. 143-153, 1994.
17. ROCKAFELLAR, R. T., Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming, SIAM Journal on Control and Optimization, Vol. 12, pp. 268-285, 1974.