Convergence rate estimates for penalty methods revisited

Izmailov, A.F.; Solodov, M.V.

Авторы: Izmailov A.F., Solodov M.V.
Журнал: Computational Optimization and Applications
Том: 85
Номер: 3
Год издания: 2023
Издательство: Springer Nature
Местоположение издательства: Switzerland
Первая страница: 973
Последняя страница: 992
DOI: 10.1007/s10589-023-00476-1
Аннотация: For the classical quadratic penalty, it is known that the distance from the solution of the penalty subproblem to the solution of the original problem is at worst inversely proportional to the value of the penalty parameter under the linear independence constraint qualification, strict complementarity, and the second-order sufficient optimality conditions. Moreover, using solutions of the penalty subproblem, one can obtain certain useful Lagrange multipliers estimates whose distance to the optimal ones is also at least inversely proportional to the value of the parameter. We show that the same properties hold more generally, namely, under the (weaker) strict Mangasarian–Fromovitz constraint qualification and second-order sufficiency (and without strict complementarity). Moreover, under the linear independence constraint qualification and strong second-order sufficiency (also without strict complementarity), we demonstrate local uniqueness and Lipschitz continuity of stationary points of penalty subproblems. In addition, those results follow from the analysis of general power penalty functions, of which quadratic penalty is a special case.
Добавил в систему: Измаилов Алексей Феридович

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Convergence rate estimates for penalty methods revisitedстатья Исследовательская статья

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