Cominetti, Roberto; Correa, Rafael Sur une dérivée de second ordre en analyse non différentiable. (On a second order directional derivative in non-differentiable analysis). (French) Zbl 0604.46049 C. R. Acad. Sci., Paris, Sér. I 303, 861-864 (1986). 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. Cited in 6 Documents MSC: 46G05 Derivatives of functions in infinite-dimensional spaces 49K27 Optimality conditions for problems in abstract spaces Keywords:second order directional derivative; bisublinearity; symmetric fan; Generalized Hessian; second order Taylor expansion; optimality PDFBibTeX XMLCite \textit{R. Cominetti} and \textit{R. Correa}, C. R. Acad. Sci., Paris, Sér. I 303, 861--864 (1986; Zbl 0604.46049)