On Second-order Conditions for Quasiconvexity and Pseudoconvexity of ${\mathcal{C}}^{1,1}$-smooth Functions

Pham Duy Khanh, Vo Thanh Phat

For a ${\mathcal{C}}^2$-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subs…