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Computing second-order points under equality constraints: revisiting Fletcher's augmented Lagrangian
Computing second-order points under equality constraints: revisiting Fletcher's augmented Lagrangian
- 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.
- Subjects :
- Mathematics - Optimization and Control
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2204.01448
- Document Type :
- Working Paper