Augmented Lagrangian Method with Alternating Constraints for Nonlinear Optimization Problems
| Autor: | Tomohiro Niimi, Siti Nor Habibah Binti Hassan, Nobuo Yamashita |
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| Rok vydání: | 2019 |
| Předmět: |
021103 operations research
Control and Optimization Augmented Lagrangian method Applied Mathematics MathematicsofComputing_NUMERICALANALYSIS Mathematics::Optimization and Control 0211 other engineering and technologies Allowance (engineering) 010103 numerical & computational mathematics 02 engineering and technology Function (mathematics) Management Science and Operations Research 01 natural sciences Nonlinear programming symbols.namesake Lagrange multiplier Constraint functions Theory of computation symbols Applied mathematics 0101 mathematics Variable (mathematics) Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications. 181:883-904 |
| ISSN: | 1573-2878 0022-3239 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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