Subgradient Method - Classical Subgradient Rules

Classical Subgradient Rules

Let be a convex function with domain . A classical subgradient method iterates

where denotes a subgradient of at . If is differentiable, then its only subgradient is the gradient vector itself. It may happen that is not a descent direction for at . We therefore maintain a list that keeps track of the lowest objective function value found so far, i.e.

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