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Convergence Analysis of Perturbed Feasible Descent Methods
Authors:Solodov  M V
Institution:(1) Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
Abstract:We develop a general approach to convergence analysis of feasible descent methods in the presence of perturbations. The important novel feature of our analysis is that perturbations need not tend to zero in the limit. In that case, standard convergence analysis techniques are not applicable. Therefore, a new approach is needed. We show that, in the presence of perturbations, a certain epsi-approximate solution can be obtained, where epsi depends linearly on the level of perturbations. Applications to the gradient projection, proximal minimization, extragradient and incremental gradient algorithms are described.
Keywords:Feasible descent methods  perturbation analysis  approximate solutions
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