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A survey on dual behavior of Newton-type methods for constrained optimizationтезисы доклада
- Авторы: Izmailov A.F., Solodov M.V.
- Сборник: The International Conference "Nonlinear Analysis and Optimization Problems"': Proceedings
- Серия: Scientific Meetings, V.100. The Section of Natural Sciences
- Том: 13
- Тезисы
- Год издания: 2009
- Место издания: Montenegrin Academy of Sciences and Arts Podgorica
- Первая страница: 157
- Последняя страница: 174
- Аннотация: For constrained optimization problems with nonunique Lagrange multiplier associated to a solution, we consider a certain thin subclass of multipliers called critical (and in particular, violating the second-order sufficient condition for optimality) that exhibits some very special properties. Specifically, convergence to a critical multiplier appears to be a typical scenario of dual behaviour of primal-dual Newton-type methods when critical multipliers do exist. Moreover, along with the possible absence of dual convergence, attraction to critical multipliers is precisely the reason for slow primal convergence usually observed on degenerate problems. On the other hand, critical multipliers turn out to have some special analytical stability properties: noncritical multipliers should not be expected to be stable subject to parametric perturbations of optimality systems.
- Добавил в систему: Измаилов Алексей Феридович