Back to Search Start Over

Computing second-order points under equality constraints: revisiting Fletcher's augmented Lagrangian

Computing second-order points under equality constraints: revisiting Fletcher's augmented Lagrangian

Authors :
Goyens, Florentin
Eftekhari, Armin
Boumal, Nicolas
Publication Year :
2022

Abstract

We address the problem of minimizing a smooth function under smooth equality constraints. Under regularity assumptions on these constraints, we propose a notion of approximate first- and second-order critical point which relies on the geometric formalism of Riemannian optimization. Using a smooth exact penalty function known as Fletcher's augmented Lagrangian, we propose an algorithm to minimize the penalized cost function which reaches $\varepsilon$-approximate second-order critical points of the original optimization problem in at most $\mathcal{O}(\varepsilon^{-3})$ iterations. This improves on current best theoretical bounds. Along the way, we show new properties of Fletcher's augmented Lagrangian, which may be of independent interest.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2204.01448
Document Type :
Working Paper