Within a cellular wireless network the unbalanced user load among cells, together with Inter-Cell-Interference (ICI), constitute major factors responsible for poor overall performance. In the current work, a novel decentralized algorithm for Load Balancing in the downlink is suggested. Two are the major novelties in the analysis. (A) The algorithm is based on the solution of a mixed integer optimization problem solved using Lagrangian but not Linear Programming relaxation, which allows the solution to be binary for the user assignment variables. (B) Its implementation is based on exchange of certain prices among base stations and allows each of them to make choices individually without the aid of a central controller. The cell handover parameters are further adequately adjusted to enforce cell-edge users to migrate to their optimal base station. The algorithm aims at optimally balancing the load, while at the same time guaranteeing low levels of ICI. Its performance is evaluated through simulations, which illustrate the improvements provided on aggregate system utility.