Approximations in Decomposition of Large-Scale Convex Programs via a Nondifferentiable Optimization Method

Abstract

A proximal bundle methcxi is presented for minimizing a nonsmooth convex function f. At each iteration it requires only one approximate evaluation of f and its £-subgradient, and finds a search direction via quadratic programming. When applied to Lagrangian decomposition of convex programs, it allows for inexact solutions of decomposed subproblems; yet, increasing their required accuracy automatically, it asymptotically ftnds both primal and dual solutions. Some encouraging numerical experience is reported.