Nonlinear Lagrangian algorithm plays an important role in solving constrained optimization problems. It is known that, under appropriate conditions, the sequence generated by the first-order multiplier iteration converges superlinearly. This paper aims at analyzing the second-order multiplier iteration based on a class of nonlinear Lagrangians for solving nonlinear programming problems with inequality constraints. It is suggested that the sequence generated by the second-order multiplier iteration converges superlinearly with order at least two if in addition the Hessians of functions involved in problem are Lipschitz continuous.
Yong-Hong Ren. "Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians." Abstr. Appl. Anal. 2014 (SI43) 1 - 7, 2014. https://doi.org/10.1155/2014/210284