396. A Variable Dimension Sketching Strategy for Nonlinear Least-Squares
Invited abstract in session WB-3: Recent Advances in Line-Search Based Optimization, stream Large scale optimization: methods and algorithms.
Wednesday, 10:30-12:30Room: B100/4011
Authors (first author is the speaker)
| 1. | Greta Malaspina
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| 2. | Stefania Bellavia
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| Dipartimento di Ingegneria Industriale, Universita di Firenze | |
| 3. | Benedetta Morini
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| Dipartimento di Ingegneria Industriale, Universita di Firenze |
Abstract
We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace is adaptive, and two strategies are considered for its update, one that is based solely on Armijo condition, and one that takes into account the true Gauss-Newton model. Under suitable assumptions on the objective function and the random subspace, we prove a probabilistic bound on the number of iterations needed by the method to reduce the norm of the gradient below any given threshold. The numerical experiments demonstrate the effectiveness of the proposed method, compared to classical Gauss-Newton method and to the method that employs random subspaces with non-adaptive dimension.
Keywords
- Stochastic optimization
- Large-scale optimization
Status: accepted
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