A nonmonotone line search method for noisy minimization

is satisfied, where σ is the noise level. Alternatively, the algorithm terminates when the maximum number of 400 ·n function evaluations is exceeded. For each problem, a series of 50 independent runs are conducted. We considered a test run successful if the stopping criterium (1) is satisfied before exceeding the maximal number of function evaluations. To compare the performance of methods from the set of methodsM over the set of problems P, the following indices (see [3]), for each method i are used. Let us denote by P̃ = {j ∈ P|∃i ∈ M, Nij > 0}, Pi = {j ∈ P|Nij > 0}, Mj = {i ∈ M|Nij > 0}, with Nij being the number of successful runs out of 50 for the method i solving the problem j. Then we have: