Gradient dynamics reveals convergence to local minima in semi-algebraic functions, indicating discrete and continuous dynamics are viable.
We show that gradient dynamics can converge to any local minimum of a semi-algebraic function. Our results cover both discrete and continuous dynamics. For discrete gradient dynamics, we show that it can converge to any local minimum once the stepsize is nonsummable and sufficiently small, and the initial value is properly chosen.
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Josz et al. (2025) studied this question.
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