Augmented Lagrangian Method with Alternating Constraints for Nonlinear Optimization Problems

Siti Nor Habibah Binti Hassan (), Tomohiro Niimi () and Nobuo Yamashita ()
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Siti Nor Habibah Binti Hassan: Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya
Tomohiro Niimi: Bank of Japan
Nobuo Yamashita: Kyoto University

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 3, No 10, 883-904

Abstract: Abstract The augmented Lagrangian method is a classical solution method for nonlinear optimization problems. At each iteration, it minimizes an augmented Lagrangian function that consists of the constraint functions and the corresponding Lagrange multipliers. If the Lagrange multipliers in the augmented Lagrangian function are close to the exact Lagrange multipliers at an optimal solution, the method converges steadily. Since the conventional augmented Lagrangian method uses inaccurate estimated Lagrange multipliers, it sometimes converges slowly. In this paper, we propose a novel augmented Lagrangian method that allows the augmented Lagrangian function and its minimization problem to have variable constraints at each iteration. This allowance enables the new method to get more accurate estimated Lagrange multipliers by exploiting Karush–Kuhn–Tucker points of the subproblems and consequently to converge more efficiently and steadily.

Keywords: Augmented Lagrangian functions; Gradient descent method; Large-scale problem; Nonlinear optimization; 26A16; 41A25; 47B36 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01488-w

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