On the Convergence Properties of a Second-Order Augmented Lagrangian Method for Nonlinear Programming Problems with Inequality Constraints

Liang Chen () and Anping Liao ()
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Liang Chen: Hunan University
Anping Liao: Hunan University

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 1, No 12, 248-265

Abstract: Abstract The objective of this paper is to conduct a theoretical study on the convergence properties of a second-order augmented Lagrangian method for solving nonlinear programming problems with both equality and inequality constraints. Specifically, we utilize a specially designed generalized Newton method to furnish the second-order iteration of the multipliers and show that when the linear independent constraint qualification and the strong second-order sufficient condition hold, the method employed in this paper is locally convergent and possesses a superlinear rate of convergence, although the penalty parameter is fixed and/or the strict complementarity fails.

Keywords: Second-order augmented Lagrangian method; Nonlinear programming; Generalized Newton method; Nonsmooth analysis; 90C30; 49J52; 65K05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-015-0842-5

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