Optimality conditions for discrete calculus of variations problems (Q941021)

Using a discrete analog of the so-called ``2-regularity condition'' instead of the better known ``Robinson condition'' in Mathematical Programming, the author obtains first order and also second order necessary optimality conditions for the problem of minimizing a cost-functional of the form: \[ \varphi (\xi):=f_0(x_0,x_N)+ \sum_0^N f(x_{i+1},x_{i+1}-x_i), \quad \xi=(x_0,x_1,\dots, x_N)\in\mathbb R^{N+1} \] subject to: \[ g_i(x_i)=0\in\mathbb R^m, \;i=0,1,\dots,N, \quad K(x_0,x_N)=0\in\mathbb R^k. \]