CARATHÉODORY CONDITIONS

Carathéodory conditions - For the classical Lagrange form, Opt(f(x): x in R^n, h(x)=0), where f, h are in C^1, the following conditions are necessary for a feasible x to be optimal : there exists (y0, y) in R^(m+1)\(0), called multipliers, such that

This reduces to the Lagrange Multiplier Rule when y0 is not zero (divide by y0), which must be the case if grad_h(x) has full row rank. Here is a biography of Carathéodory .