Lagrange multipliers and generalized differentiable functions in vector extremum problems (Q1114596)

We establish a necessary optimality condition for a nondifferentiable vector extremum problem which involves a generalized vector-valued Lagrangian function. Such a condition is stated for a wide class of functions, which embraces the differentiable ones and a subclass of locally Lipschitzian functions. The condition embodies the classic theorem of F. John in multiobjective optimization.