Global convergence of the Newton interior-point method for nonlinear programming
This paper studies the Newton interior-point algorithm presented in \textit{A. S. El-Bakry, R. A. Tapia, T. Tsuchiya} and \textit{Y. Zhang} [J. Optimization Theory Appl. 89, No. 3, 507--541 (1996; Zbl 0851.90115)]. The main result is to prove the global convergence of this algorithm under weaker assumptions. The original global convergence result in El-Bakry, et. al. used four hypothesis. In the new result the last one concerning the linear independency of the gradients of some inequality constraints is changed by the boundedness of the sequence of multipliers associated to nontrivial constraints. It is also proved that the original assumptions are sufficient for the new one. Finally some numerical results are given in order to show that new assumption is actually weaker.
scientific article; zbMATH DE number 2073492