Let X = (X n ) be a stationary process of k × k real-valued matrices, depending on some vector-valued parameter θeRp, satisfying E log+ ||.X 0 (θ)|| n 1/n E log || X n · X n−1 … · X 0 ||. Top-Lyapunov exponents play a prominent role in randomization procedures for optimization, such as SPSA, and in finance, giving the growth-rate of a self-financing currency-portfolio with a fixed strategy. We develop a convergent iterative procedure for the optimization of λ(θ). In the case when X is a Markov-process, the proposed procedure is formally within the class defined in [1], however the general case requires fundamentally different techniques.