An optimization problem \(\min f(x)\), \(x\in X\), is considered where \(f(x)\) may he evaluated with essential errors only. An approximation method is proposed where at each iteration an approximation \(f^ k(x)\) of \(f(x)\) is used. The combinations of the approximation method with reduced gradient, feasible direction and Lagrange multiplier algorithms are analyzed, and convergence theorems are formulated. The obtained results are applied to stochastic programs with recourse.