The subgradient method is an optimization technique used to minimize non-differentiable convex functions. While traditional gradient descent is applicable to differentiable functions, many optimization problems involve functions that are not smooth or do not have well-defined gradients everywhere. In such cases, subgradients provide a useful alternative.
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The subgradient method minimizes a possibly nonsmooth convex function by choosing and iteratingIf the subgradients are bounded by and a minimizer is within distance of , a suitable constant or diminishing step size finds objective error at most in iterations.