Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians

Abstract EN

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.