A.R. Conn, Nick Gould, et al.
Mathematics of Computation
Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In this paper, we design and analyze stochastic inexact augmented Lagrangian methods (Stoc-iALM) to solve problems involving a nonconvex composite (i.e. smooth + nonsmooth) objective and nonconvex smooth functional constraints. We adopt the standard iALM framework and design a subroutine by using the momentum-based variance-reduced proximal stochastic gradient method (PStorm) and a postprocessing step. Under certain regularity conditions (assumed also in existing works), to reach an ε -KKT point in expectation, we establish an oracle complexity result of O(ε- 5) , which is better than the best-known O(ε- 6) result. Numerical experiments on the fairness constrained problem and the Neyman–Pearson classification problem with real data demonstrate that our proposed method outperforms an existing method with the previously best-known complexity result.
A.R. Conn, Nick Gould, et al.
Mathematics of Computation
Moutaz Fakhry, Yuri Granik, et al.
SPIE Photomask Technology + EUV Lithography 2011
Matthew A Grayson
Journal of Complexity
Daniel J. Costello Jr., Pierre R. Chevillat, et al.
ISIT 1997