A nonmonotone line search method for noisy minimization

A nonmonotone line search method for optimization in noisy environment is proposed. The method is defined for arbitrary search directions and uses only the noisy function values. Convergence of the proposed method is established under a set of standard assumptions. The computational issues are considered and the presented numerical results affirm that nonmonotone strategies are worth considering. Four different line search rules with three different directions are compared numerically. The influence of nonmonotonicity is discussed.