Inexact subgradient methods with applications in stochastic programming (Q1315432)

Projected gradient-type methods are considered for minimizing a function \(f\) on a given subset \(X\) of \(\mathbb{R}^ n\), where the negative step direction \(\xi^ k\) is a subgradient of \(f_ k\) with a sequence \((f_ k)\) of objective function approximations. Sufficient conditions are given for the convergence of this algorithm to the set of optimal solutions. Furthermore, based on the approximations \(f_ k\), methods for the adaptive selection of the step sizes \(s_ k\) are given. The method is applied to the solution of two-stage stochastic linear programs.