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Global convergence of the Heavy-ball method for convex optimization

Euhanna Ghadimi(euhanna***at***kth.se)
Hamid Reza Feyzmahdavian(hamidrez***at***kth.se)
Mikael Johansson(mikaelj***at***kth.se)

Abstract: This paper establishes global convergence and provides global bounds of the convergence rate of the Heavy-ball method for convex optimization problems. When the objective function has Lipschitz-continuous gradient, we show that the Cesa ́ro average of the iterates converges to the optimum at a rate of $O(1/k)$ where k is the number of iterations. When the objective function is also strongly convex, we prove that the Heavy-ball iterates converge linearly to the unique optimum.

Keywords: Performance of first-order algorithms, Rate of convergence, Complexity, Smooth convex optimization, Heavy-ball method, Gradient Descent

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Unconstrained Optimization )


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Entry Submitted: 12/23/2014
Entry Accepted: 12/23/2014
Entry Last Modified: 12/23/2014

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