Abstract
The purpose of this work is two-fold. First, we present the spectral-step subgradient method to solve nonsmooth unconstrained optimization problems. It combines the classical subgradient approach and a nonmonotone linesearch with the spectral step length, which does not require any previous knowledge of the optimal value. We focus on the interesting case in which the objective function is convex and continuously differentiable almost everywhere, and it is often non-differentiable at minimizers. Secondly, we use performance profiles to compare the spectral-step subgradient method with other subgradient methods. This comparison will allow us to place the spectral-step subgradient algorithm among other subgradient algorithms.
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