Approaches for performing simulation optimization for solving a constrained optimization problem are generally disclosed. One embodiment according to the present disclosure is to formulate a Lagrange equation having incorporated a Lagrange parameter, a first long run average function for an objective associated with the constrained optimization problem, and a second long run average function for a constraint associated with the constrained optimization problem. Then, to identify a parameter value that may lead to an extreme value for the Lagrange equation, in an iterative manner, averages of the first long run average function and the second long run average function are calculated, a gradient of the Lagrange equation is estimated, and the Lagrange parameter is updated.