Optimization based on information containing uncertainties

Considers the problem of finding extrema of an unknown function L(⋅):I R^l× R or the root set of its gradient f(⋅) ^{\underline \underline Δ} ▽ L(⋅) on the basis of observations, which may contain two kinds of uncertainties: random noise and structural uncertainties. The latter is caused by the fact that observations may not be made on the recent estimate, may not even be carried out on f(⋅) but on some other function. The optimization algorithm and conditions guaranteeing its convergence are given.