The possibility of applying Linear or Quadratic Programming to the problem of optimizing nuclear reactor fuel recycle, is investigated. It is demonstrated, that the methods mentioned, may be applied successfully to a simplified model of a nuclear reactor. An appropriate representation of the fuel recycle as a feedback control system is proposed. An iterative algorithm to establish the refueling times, which are unknown a priori, is formulated and implemented to some specific examples. The convergence of the algorithm, proposed in this paper, has been established numerically.