A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization
For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher's augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this paper, the analysis of this algorithm is extended, offering a two-fold contribution. First, it is shown that a local-linear rate of convergence can be obtained by this method if it is initiated sufficiently close to a strong second-order stationary point and employs a sufficiently small step-size parameter and sufficiently large penalty parameter. In this case, the algorithm r...
| Authors | Frank E. Curtis, Lingjun Guo, Daniel P. Robinson |
|---|---|
| Primary category | math.OC |
| Published | 12 August 2026 |
| Last updated at source | 12 August 2026 |
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