In this talk we discuss ergodic optimization problems for subadditive sequences of functions on a topological dynamical system. We show that for $t\rightarrow \infty$ any accumulation point of a family of equilibrium states is a maximizing measure. We also show that the Lyapunov exponent and entropy of equilibrium states converges in the limit $t\rightarrow \infty$ to the maximum Lyapunov exponent and entropy of maximizing measures.