Epsilon-proximal decomposition method
The paper is concerned with a modification of a proximal decomposition method for minimizing a convex function over a subspace of \(\mathbb R^n\). In order to obtain a numerically suitable quadratic problem, which provides an approximation for the proximal step, the proximal decomposition method is combined with a bundle strategy. The resulting algorithmic scheme fits the general framework of Rockafellar's inexact proximal-point algorithm. Next a practical algorithm is developed which is based on recent ideas by \textit{M.V. Solodov} and \textit{B.F. Svaiter} [Set-Valued Analysis 7, 323--345 (1999; Zbl 0959.90038)]. It turns out that the approach is particularly useful when the objective function is a sum of convex functions. In that case, the quadratic subproblem in the algorithm splits into a number of smaller quadratic problems which, via parallel solution, could make the approach attractive for large-scale problems. Examples considered are a new stabilized version of Benders decomposition method and nonlinear convex multicommodity flow problems.
scientific article; zbMATH DE number 2055183