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We develop subgradient- and gradient-based methods for minimizing stronglyconvex functions under a notion which generalizes the standard Euclidean strongconvexity. We propose a unifying framework for subgradient methods which yieldstwo kinds of methods, namely, the Proximal Gradient Method (PGM) and theConditional Gradient Method (CGM), unifying several existing methods. Theunifying framework provides tools to analyze the convergence of PGMs and CGMsfor non-smooth, (weakly) smooth, and further for structured problems such asthe inexact oracle models. The proposed subgradient methods yield optimal PGMsfor several classes of problems and yield optimal and nearly optimal CGMs forsmooth and weakly smooth problems, respectively.

New results on subgradient methods for strongly convex optimization problems with a unified analysis