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Sur une dérivée de second ordre en analyse non différentiable. (On a second order directional derivative in non-differentiable analysis). (French) Zbl 0604.46049
We introduce a new second order directional derivative for real valued functions defined on a locally convex topological vector space. The bisublinearity of this derivative enable us to associate it with a symmetric fan which we will be called Generalized Hessian. We obtain by this way a second order Taylor expansion and optimality conditions involving these derivatives.

46G05 Derivatives of functions in infinite-dimensional spaces
49K27 Optimality conditions for problems in abstract spaces