Abstract

We consider the diagonal inexact proximal point iteration uk - uk-1/?k ? - ? ? k f (uk, rk) + vk where f(x, r) = cTx + r ? exp[(Aix -bi)/r] is the exponential penalty approximation of the linear program min(cTx : Ax ? b}. We prove that under an appropriate choice of the sequences ?k, ?k and with some control on the residual vk, for every rk ? 0+ the sequence uk converges towards an optimal point u? of the linear program. We also study the convergence of the associated dual sequence ?ik = exp[(Aiuk - bi) / rk] towards a dual optimal solution.