Approximations in proximal bundle methods and decomposition of convex programs

摘要: A proximal bundle method is presented for minimizing a nonsmooth convex functionf. At each iteration, it requires only one approximate evaluation off and its e-subgradient, finds search direction via quadratic programming. When applied to the Lagrangian decomposition of programs, allows inexact solutions decomposed subproblems; yet, increasing their required accuracy automatically, asymptotically both primal dual solutions. It an implementable version point algorithm. Some encouraging numerical experience reported.