Abstract
A necessary and sufficient criterion for the extremum of a function is given where the function is differentiable in a certain neighbourhood, but only continuous at the extremum itself. This slight generalization of a well-known criterion is an useful instrument in economic theory because many used functions are not differentiable on the coordinate hyperplanes, especially not at the origin.
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References
Bazaraa, M.S., J.J. Goode, andC.M. Shetty: Optimality Criteria in Nonlinear Programming without Differentiability. Operations Research19, 1971, 77–86.
Inada, K.: On a Two-Sector Model of Economic Growth: Comments and a Generalization. Review of Economic Studies30, 1963, 119–127.
Mangasarian, O.L.: Nonlinear Programming. New York 1969.
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I am grateful to an anonymous referee for some corrections and improvements.
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Dyckhoff, H. An optimality criterion for problems without differentiability on the boundary. Zeitschrift für Operations Research 25, 167–169 (1981). https://doi.org/10.1007/BF01919301
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DOI: https://doi.org/10.1007/BF01919301