This paper presents a stochastic recursive procedure under constraints to
find the optimal distance at which an agent must post his order to minimize his
execution cost. We prove the $a.s.$ convergence of the algorithm under
assumptions on the cost function and give some practical criteria on model
parameters to ensure that the conditions to use the algorithm are fulfilled
(using notably principle of opposite monotony). We illustrate our results with
numerical experiments on simulated data but also by using a financial market
dataset.