This paper presents a unifying and systematic framework to solve wireless max-min utility fairness optimization problems in multiuser wireless networks with generalized monotonic constraints. These problems are often challenging to solve due to their nonlinearity and non-convexity. Our framework leverages a general result in nonlinear Perron-Frobenius theory to characterize the global optimal solution of these problems analytically, and to design scalable and fast-convergent algorithms for the computation of the optimal solution. This work advances the state-of-the-art in handling wireless utility optimization problems with nonlinear monotonic constraints, which existing methodologies cannot handle, and also unifies previous works in this area. Several representative applications are considered to illustrate the effectiveness of the proposed framework, including max-min quality of service subject to robust interference temperature constraints in cognitive radio networks, min-max outage subject to outage constraints in heterogeneous networks, and min-max weighted MSE subject to SINR constraints in multiuser downlink system.