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The starting assumptions to study the convergence and complexity ofgradient-type methods may be the smoothness (also called Lipschitz continuityof gradient) and the strong convexity. In this note, we revisit these two basicproperties from a new perspective that motivates their definitions andequivalent characterizations, along with an improved linear convergence of thegradient descent method.

New insights in smoothness and strong convexity with improved convergence of gradient descent