Second-order optimality conditions for finite-dimensional smooth and nonsmooth nonlinear programming are obtained by a new method that emphasizes a close connection with geometrical approximation of ...

We construct unconditionally stable, unconditionally uniquely solvable, and secondorder accurate (in time) schemes for gradient flows with energy of the form ∫ Ω (F (∇ø (×)) + $\frac { { { \in ^2}}} ...