Monday, 15:15 - 15:40 h, Room: H 0110


Mikhail Solodov
Convergence properties of augmented Lagrangian methods under the second-order sufficient optimality condition

Coauthor: Damian Fernandez


We establish local convergence and rate of convergence
of the classical augmented Lagrangian algorithm
under the
sole assumption that the dual starting point is close to a
multiplier satisfying the second-order sufficient optimality condition (SOSC).
No constraint qualifications
of any kind are needed. Previous literature on the subject
required, in addition, the linear independence constraint qualification and
either strict complementarity or a stronger
version of SOSC.
Using only SOSC, for
penalty parameters large enough we prove primal-dual Q-linear
convergence rate, which becomes superlinear if the parameters are allowed
to go to infinity. Both exact and inexact solutions of subproblems
are considered. In the exact case, we further show that the
primal convergence rate is of the same Q-order as the primal-dual rate.
Previous assertions
for the primal sequence all had to do with the the weaker
R-rate of convergence and required the stronger assumptions
cited above. Finally, we show that under our assumptions one of the popular rules
of controlling the penalty parameters ensures they stay bounded.


Talk 1 of the invited session Mon.3.H 0110
"Nonlinear optimization III" [...]
Cluster 16
"Nonlinear programming" [...]


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