Descent methods with linesearch in the presence of perturbations (Q1360171)

The authors consider the class of descent algorithms for the unconstrained optimization problem \[ \min_{x\in\mathbb{R}^n} f(x), \] where \(f\in\mathbb{R}^n\to \mathbb{R}\) is a differentiable function with a Hölder continuous gradient, in the case when the gradient of the objective function is computed inexactly. A modified Armijo-type rule for computing the stepsize is proposed which guarantees that the algorithm obtains a reasonable approximate solution. The authors give neither applications nor examples for the algorithm.