On the global convergence of interior-point nonlinear programming algorithms

Carathéodory's lemma states that if we have a linear combination of vectors in n, we can rewrite this combination using a linearly independent subset. This lemma has been successfully applied in nonlinear optimization in many contexts. In this work we present a new version of this celebrated result, in which we obtained new bounds for the size of the coefficients in the linear combination and we provide examples where these bounds are useful. We show how these new bounds can be used to prove that the internal ...