Characterization of R-Evenly Quasiconvex Functions
- 66 Downloads
A function defined on a locally convex space is called evenly quasiconvex if its level sets are intersections of families of open half-spaces. Furthermore, if the closures of these open halfspaces do not contain the origin, then the function is called R-evenly quasiconvex. In this note, R-evenly quasiconvex functions are characterized as those evenly-quasiconvex functions that satisfy a certain simple relation with their lower semicontinuous hulls.
Unable to display preview. Download preview PDF.
- 1.THACH, P. T., Diewert-Crouzeix Conjugation for General Quasiconvex Duality and Applications, Journal of Optimization Theory and Applications, Vol. 86, pp. 719–743, 1995.Google Scholar
- 2.DIEWERT, W. E., Duality Approaches to Microeconomic Theory, Handbook of Mathematical Economics, Edited by K. J. Arrow and M. D. Intriligator, North Holland, Amsterdam, Netherlands, Vol. 2, pp. 535–599, 1982.Google Scholar
- 3.FENCHEL, W., A Remark on Convex Sets and Polarity, Communications du Séminaire Mathématique de l'Université de Lund, Supplement, pp. 82–89, 1952.Google Scholar
- 4.MARTINEZ-LEGAZ, J. E., A Generalized Concept of Conjugation, Optimization: Theory and Algorithms, Edited by A. Auslender, J. B. Hiriart-Urruty, and W. Oettli, Marcel Dekker, New York, New York, pp. 45–59, 1983.Google Scholar
- 5.PASSY, U., and PRISMAN, E. Z., Conjugacy in Quasiconvex Programming, Mathematical Programming, Vol. 30, pp. 121–146, 1984.Google Scholar
- 6.MARTINEZ-LEGAZ, J. E., Quasiconvex Duality Theory by Generalized Conjugation Methods, Optimization, Vol. 19, pp. 603–652, 1988.Google Scholar
- 7.MARTINEZ-LEGAZ, J. E., Duality between Direct and Indirect Utility Functions under Minimal Hypotheses, Journal of Mathematical Economics, Vol. 20, pp. 199–209, 1991.Google Scholar
- 8.MARTINEZ-LEGAZ, J. E., and SANTOS, M. S., Duality between Direct and Indirect Preferences, Economic Theory, Vol. 3, pp. 335–351, 1993.Google Scholar
- 9.CROUZEIX, J. P., Continuity and Differentiability Properties of Quasiconvex Functions on R n, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 109–130, 1982.Google Scholar
- 10.HOLMES, R. B., Geometric Functional Analysis and Its Applications, Springer Verlag, New York, New York, 1975.Google Scholar