The problem of maximizing a utility function while limiting the outage probability below an appropriate threshold is investigated. A coded-division multi access wireless network under mixed Nakagami-lognormal fading is considered. Solving such a utility maximization problem is difficult because the problem is non-convex and non-geometric with mixed integer and real decision variables and no explicit functions of the constraints are available. In this paper, two methods to the solution of the utility maximization problem are proposed. By the first method, a simple explicit outage approximation is used and the constraint that rates are integers is relaxed yielding a standard convex programming optimization that can be solved quickly but at the price of a reduced accuracy. The second method uses a more accurate outage approximation, which allows one solving the utility maximization problem by the Lagrange duality for non-convex problems and contraction mapping theory. Numerical results show that the first method performs well for average values of the outage requirements, whereas the second one is always more accurate, but is also more computationally expensive.