  We develop subgradient- and gradient-based methods for minimizing strongly
convex functions under a notion which generalizes the standard Euclidean strong
convexity. We propose a unifying framework for subgradient methods which yields
two kinds of methods, namely, the Proximal Gradient Method (PGM) and the
Conditional Gradient Method (CGM), unifying several existing methods. The
unifying framework provides tools to analyze the convergence of PGMs and CGMs
for non-smooth, (weakly) smooth, and further for structured problems such as
the inexact oracle models. The proposed subgradient methods yield optimal PGMs
for several classes of problems and yield optimal and nearly optimal CGMs for
smooth and weakly smooth problems, respectively.
