Functional optimization through semilocal approximate minimization

An approach based on semilocal approximation is introduced for the solution of a general class of operations research problems, such as Markovian decision problems, multistage optimal control, and maximum-likelihood estimation. Because it is extremely hard to derive analytical solutions that minimize the cost in most instances of the problem, we must look for approximate solutions. Here, it is shown that good solutions can be obtained with a moderate computational effort by exploiting properties of semilocal approximation through kernel models and efficient sampling of the state space. The convergence of the proposed method, called semilocal approximate minimization (SLAM), is discussed, and the consistency of the solution is derived. Simulation results show the efficiency of SLAM, also through its application to a classic operations research problem, i.e., inventory forecasting.