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# Strong Convexity and Its Generalization

## Introduction

The convex condition of the objective function guarantees extrema uniqueness. It says that if $f$ is convex, we can discuss the convergence rate of optimization methods by estimating $||f(w_t)-f^{opt}||$, where $f^{opt}$ is the global maximum/minimum (optimum). Otherwise, we know nothing about the distance and only discuss $\min_{t\in\{0,1,\dots,T\}}||\nabla f(w^t)||^{2}$.

“夕阳余晖，淡淡霞光中的红蜻蜓。