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Session II.2 - Continuous Optimization

Friday, June 16, 15:00 ~ 15:30

Non-convex optimization when the solution is not unique: A kaleidoscope of favorable conditions

Nicolas Boumal

EPFL, Switzerland   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Classical optimization algorithms can see their local convergence rates deteriorate when the Hessian at the optimum is singular. The latter is inescapable when the optima are non-isolated. Yet, several algorithms behave perfectly nicely even when optima form a continuum (e.g., due to overparameterization). This has been studied through various lenses, including the Polyak-Lojasiewicz condition, Quadratic Growth, the Error Bound, and (less so) through a Morse-Bott property. I will present old and new links between all four of these, and touch on implications for fast local convergence of classical algorithms.

Joint work with Quentin Rebjock (EPFL).

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