The smoothness condition refers to a property of functions that ensures they are continuously differentiable, which is crucial for the convergence of optimization algorithms. This property guarantees that the gradient of the function does not change too abruptly, enabling methods such as steepest descent to effectively navigate towards local minima. Smoothness conditions often relate to concepts such as Lipschitz continuity, which further characterizes how functions behave in the vicinity of their input values.
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