We study the class Q of quasiconvex functions (i.e. functions with convex sublevel sets), by associating to every quasi convex function u a function H :R^n × R→R ∪ {±∞}, such that H(X, t) is nondecreasing in t and sublinear in X: for every fixed t , the function H(·, t) is nothing else than the support function of the sublevel set {x ∈ R^n: u(x)<t}. When u is suitably regular, we establish an exact relation between the Hessian matrices of u and H; this allows us to find explicit formulae to write the k-Hessian operators of u in terms of H. Then we investigate on Minkowski addition of quasiconvex functions.

On the Hessian matrix and Minkowski addition of quasiconvex functions / M. LONGINETTI; P. SALANI. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 88:(2007), pp. 276-292. [10.1016/j.matpur.2007.06.007]

On the Hessian matrix and Minkowski addition of quasiconvex functions

LONGINETTI, MARCO;SALANI, PAOLO
2007

Abstract

We study the class Q of quasiconvex functions (i.e. functions with convex sublevel sets), by associating to every quasi convex function u a function H :R^n × R→R ∪ {±∞}, such that H(X, t) is nondecreasing in t and sublinear in X: for every fixed t , the function H(·, t) is nothing else than the support function of the sublevel set {x ∈ R^n: u(x)
2007
88
276
292
M. LONGINETTI; P. SALANI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/256204
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