52. TRFD: A derivative-free trust-region method based on finite differences for composite nonsmooth optimization
Invited abstract in session MD-1: Derivative-Free Optimization Methods for challenging applications: Handling Nonsmoothness and Constraints, stream Zeroth and first-order optimization methods.
Monday, 16:30-18:30Room: B100/1001
Authors (first author is the speaker)
| 1. | Dânâ Davar
|
| Applied Mathematics, UCLouvain | |
| 2. | Geovani Grapiglia
|
| Applied Mathematics, Université catholique de Louvain |
Abstract
We present TRFD, a derivative-free trust-region method based on finite differences for minimizing composite nonsmooth functions. We establish a worst-case evaluation complexity bound that TRFD needs to find an approximate stationary point. For L1 and Minimax problems, the bound depends linearly on the number of variables for specific instances of TRFD, while this bound depends quadratically on the inverse of the desired accuracy. In addition, if the objective function is convex, the previous complexity can be improved for Minimax problems to a linear dependence on the inverse of the desired accuracy. Numerical results are also reported, illustrating the relative efficiency of TRFD.
Keywords
- Derivative-free optimization
- Complexity and efficiency of algorithms
- Non-smooth optimization
Status: accepted
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