A Levenberg-Marquardt method with approximate projections
| Autor: | Andreas Fischer, Alfredo N. Iusem, Markus Herrich, Roger Behling, Yinyu Ye |
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| Rok vydání: | 2013 |
| Předmět: |
Quadratic growth
Mathematical optimization Control and Optimization Applied Mathematics Solution set Regular polygon Physics::Data Analysis Statistics and Probability System of linear equations Levenberg–Marquardt algorithm Computational Mathematics Computer Science::Computational Engineering Finance and Science Convergence (routing) Special case Constrained equation Mathematics |
| Zdroj: | Computational Optimization and Applications. 59:5-26 |
| ISSN: | 1573-2894 0926-6003 |
| DOI: | 10.1007/s10589-013-9573-4 |
| Popis: | The projected Levenberg-Marquardt method for the solution of a system of equations with convex constraints is known to converge locally quadratically to a possibly nonisolated solution if a certain error bound condition holds. This condition turns out to be quite strong since it implies that the solution sets of the constrained and of the unconstrained system are locally the same. Under a pair of more reasonable error bound conditions this paper proves R-linear convergence of a Levenberg-Marquardt method with approximate projections. In this way, computationally expensive projections can be avoided. The new method is also applicable if there are nonsmooth constraints having subgradients. Moreover, the projected Levenberg-Marquardt method is a special case of the new method and shares its R-linear convergence. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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