Resumen de Comments on: Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it 2

J.M. Martínez

• Consider the minimization of x2 subject to x2=0 . The solution of this trivial problem is x∗=0 . This solution satisfies the Lagrange (KKT) conditions and every λ∈IR is an admissible Lagrange multiplier. One of these multipliers ( λ∗=−1 ) has undersirable properties: the distance between (x∗,λ∗) and (x,λ) is not bounded by a multiple of the norm of the KKT system computed at (x,λ) . This means that the norm of the KKT system is not a safe estimator or the primal–dual distance to the solution. Roughly speaking, multipliers with this characteristic are said to be critical. The paper by Izmailov and Solodov surveys all the present knowledge about critical multipliers.