An inexact proximal-point penalty algorithm finds ε-stationary points of non-convex constrained problems in O~(ε^{-5/2}) steps with convex constraints and O~(ε^{-3}) to O~(ε^{-4}) steps with non-convex constraints.
Complexity and performance of an Augmented Lagrangian algorithm
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abstract
Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Mart\'{\i}nez and M. L. Schuverdt, On Augmented Lagrangian methods with general lower-level constraints, SIAM Journal on Optimization 18, pp. 1286-1309, 2008]. Complexity results that report its worst-case behavior in terms of iterations and evaluations of functions and derivatives that are necessary to obtain suitable stopping criteria are presented in this work. In addition, the computational performance of a new version of the method is presented, which shows that the updated software is a useful tool for solving large-scale constrained optimization problems.
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Inexact Proximal-Point Penalty Methods for Constrained Non-Convex Optimization
An inexact proximal-point penalty algorithm finds ε-stationary points of non-convex constrained problems in O~(ε^{-5/2}) steps with convex constraints and O~(ε^{-3}) to O~(ε^{-4}) steps with non-convex constraints.