Consider min{ 1 2 xQx : Ax = 0}, where Q is a positive definite matrix and A Rmn, and let x be a local minimum that is a regular point. Let be the associated Lagrange multiplier, and assume that the Hessian 2 xxL(x, ) is positive definite, where L(x, ) = 1 2 xQx Ax is the Lagrangian function. Consider the multipliers method k 1 = k Axk, where xk argminxB(x,) L(x, k), for some suitable local neighborhood B(x, ) = {x : x x }. Show that there exists a threshold > 0 and a sphere centered at such that if 0 belongs to this sphere and (0, ), then k converges to