Line search methods are very effective in practice for speeding up first-order methods for minimizing smooth functions. The step size found by a line-search procedure during each iteration can be regarded as the reciprocal of a local Lipschitz constant. We show that the convergence speed of first-order methods equipped with a simple line-search procedure depends on the harmonic mean of the local Lipschitz constants.<\/p>\n","protected":false},"excerpt":{"rendered":"
Line search methods are very effective in practice for speeding up first-order methods for minimizing smooth functions. The step size found by a line-search procedure during each iteration can be regarded as the reciprocal of a local Lipschitz constant. We show that the convergence speed of first-order methods equipped with a simple line-search procedure depends 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