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Tangent sets to unilateral convex sets. (English. Abridged French version) Zbl 0866.49026
The authors give formulas for the inner and outer second order tangent sets to some cones of nonnegative real valued functions, namely the cone of nonnegative functions defined over a compact metric space and the positive cone of \(L^p (S)\), where \(S\) is a measured space and \(1\leq p<\infty\). They give partial indications in the case \(p=\infty\).
The second order tangent sets appear in the expression of second order optimality conditions as well as sensitivity analysis of optimization problems. Therefore it is important to have explicit formulas such as those of this paper when performing a second order analysis on specific examples.

49J52 Nonsmooth analysis
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
49K99 Optimality conditions
90C31 Sensitivity, stability, parametric optimization
52A40 Inequalities and extremum problems involving convexity in convex geometry