On the Hessian matrix and Minkowski addition of quasiconvex functions

@inproceedings{Longinetti2007OnTH,
  title={On the Hessian matrix and Minkowski addition of quasiconvex functions},
  author={Marco Longinetti and Paolo Salani},
  year={2007}
}
Abstract We study the class Q of quasiconvex functions (i.e. functions with convex sublevel sets), by associating to every u ∈ Q ∩ C ( R n ) 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 D 2 u and D 2 H ; this allows us to find explicit… CONTINUE READING

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