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

2022/04/04 by Goyens, Florentin, Eftekhari, Armin, Boumal, Nicolas · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2204.01448

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 ε-approximate second-order critical points of the original optimization problem in at most O(ε^-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.

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• Progressively Sampled Equality-Constrained Optimization

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