In wireless cellular networks that are interference-limited, a variety of power control problems can be formulated as nonlinear optimization with a system-wide objective subject to many QoS constraints from individual users. Previous work have been done in the high SIR regime by solving these problems with nonlinear objectives and constraints as geometric programs. However, in the medium to low SIR regime, these problems cannot be transformed into tractable convex optimization problems. This paper makes two contributions: (1) In the low SIR regime, we propose a method with centralized computation to obtain the globally optimal solution by solving a series of geometric programs. (2) While efficient and robust algorithms have been extensively studied for centralized solutions of geometric programs, distributed algorithms have not been investigated before this paper. We present a systematic method of distributed algorithms for power control based on geometric programs in high SIR regime. These two contributions can be readily combined to distributively solve nonlinear power control problems in general SIR regime