Some remarks on lower hemicontinuity of convex multivalued mappings

Piotr, Maćkowiak (2004): Some remarks on lower hemicontinuity of convex multivalued mappings. Published in: Economic Theory , Vol. 28, No. 1 (2006): pp. 227-233.

Abstract

For a multifunction a condition sufficient for lower hemicontinuity is presented. It is shown that under convexity of graph it is possible for a multifunction to be not continuous only when a special representation of points of its domain is not feasible.

• Item Type: MPRA Paper
• Language: English
• Keywords: Convexity; Polytope; Lower hemicontinuity
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

Berge C.: Topological spaces. Oliver and Boyd, Edinburgh and London: 1963

Dutta P., Mitra T.: On Continuity of the Utility Function in Intertemporal Allocation Models: an Example. International Economic Review 30, 527-536 (1989)

Gale D., Klee V., Rockafellar T.: Convex Functions on Convex Polytopes. Proceedings of the American Mathematical Society 19, 867-873 (1968)

Florenzano M., Le Van C.: Finite Dimensional Convexity and Optimization. Berlin New~York: Springer 2001

Lucas R., Stokey N.: Recursive Methods in Economic Dynamics. Cambridge New~York: University Press 1989

McKenzie L.: Optimal economic growth, turnpike theorems and comparative dynamics. In Arrow, K., Intriligator, M. (eds.) Handbook of Mathematical Economics, Vol. III, pp. 1281-1353, Amsterdam New~York Oxford: North-Holland 1986

Rockafellar R.T.: Convex Analysis. Princeton New Jersey: Princeton University Press 1970

Rockafellar R.T., Wets R.: Variational Analysis. Berlin Heidelberg New York: Springer 1998