  We propose a new methodology to design first-order methods for unconstrained
strongly convex problems. Specifically, instead of tackling the original
objective directly, we construct a shifted objective function that has the same
minimizer as the original objective and encodes both the smoothness and strong
convexity of the original objective in an interpolation condition. We then
propose an algorithmic template for tackling the shifted objective, which can
exploit such a condition. Following this template, we derive several new
accelerated schemes for problems that are equipped with various first-order
oracles and show that the interpolation condition allows us to vastly simplify
and tighten the analysis of the derived methods. In particular, all the derived
methods have faster worst-case convergence rates than their existing
counterparts. Experiments on machine learning tasks are conducted to evaluate
the new methods.
