##### Department of Mathematics,

University of California San Diego

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### Math 278C: Optimization and Data Science

## Dr. Lexiao Lai

#### Columbia University

## Global stability of first-order methods for coercive tame functions

##### Abstract:

We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that if the method is approximated by subgradient trajectories, then the iterates eventually remain in a neighborhood of a connected component of the set of critical points. Under suitable method-dependent regularity assumptions, this result applies to the subgradient method with momentum, the stochastic subgradient method with random reshuffling and momentum, and the random-permutations cyclic coordinate descent method.

Host: Jiawang Nie

### October 4, 2023

### 3:00 PM

APM 7321

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