… Heavyball method on convex optimization problems with Lipschitzcontinuous gradient, with
and without the additional assumption of strong convexity… for quadratic programming,” Naval …

… The schemes of Nesterov [24] and Siegel [30] and the ones introduced in this paper are
built to be as efficient as possible for strongly convex functions (but not for quadratic functions). …

… The parameters are chosen to the values that provide the optimal convergence rate for the
class of convex quadratic functions in S(m, L) [10], [… The Heavy-ball method can be written as: …

… We then examine the situation of convex and strongly convex potentials and … problem is
more involved and we propose a result for the quadratic error only when f is a quadratic function (…

… on the classical Heavy-ball method for convex quadratic minimization. The … problem at
hand instead of problem parameters such as a few eigenvalues of the Hessian of the problem. …

… number of the objective function, these methods guarantee a fast exponential … Heavy
Ball schemes) is relevant in a relaxed setting, ie for composite functions satisfying a quadratic …

… are able to construct a Lyapunov function that demonstrates an \(O(1/k^2)\) rate for Heavy-ball
in the case of convex quadratic problems. Our novel proof technique, though restricted to …

… averaged version of Heavy-Ball method (AHB). We show that for quadratic problems
AHB has a … Moreover, for general convex and strongly convex functions, we prove non-accelerated …

… heavy-ball (HB) method provably does not reach an accelerated convergence rate on smooth
strongly convex problems. … of convex quadratic functions, or the set of strongly convex and …

… A lower complexity bound on the convergence of any first-order method is provided in Section
2.2. In Section 2.3, we introduce the heavy-ball method under consideration and prove its …