Abstract
Continuity and differentiability of monotone functions of several variables are studied; in particular, it is proved that these functions are almost everywhere differentiable. Then it is shown how some properties of Lipschitz functions and quasiconvex functions can be straightforwardly derived from properties of monotone functions.
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References
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© 1987 The Mathematical Programming Society, Inc.
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Chabrillac, Y., Crouzeix, JP. (1987). Continuity and differentiability properties of monotone real functions of several real variables. In: Cornet, B., Nguyen, V.H., Vial, J.P. (eds) Nonlinear Analysis and Optimization. Mathematical Programming Studies, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121151
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DOI: https://doi.org/10.1007/BFb0121151
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