FRITZ JOHN CONDITIONS

Fritz John conditions - These extend Carathéodory's conditions to deal with inequality constraints:

Suppose x* is in argmax(f(x): x in R^n, g(x) <= 0), where f and g are in C^1. Then, there exists multipliers (y0, y) >= 0, not all zero, such that y0 grad_f(x) - y grad_g(x) = 0 and yg(x) = 0.

Note that y0=1 yields the usual Kuhn-Tucker conditions .