Before revision: We develop a line-search second-order algorithmic framework for optimization problems in noisy environments, i. e., assuming that only noisy values are available for the objective function and its gradient and Hessian. In the general noisy case, almost sure convergence of the methods fitting into the framework is proved when line searches and suitably decaying step lengths are combined.
After revision: We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into the framework is proved when line searches and suitably decaying step lengths are combined.