Modern multi-core processors use power management techniques such as dynamic voltage and frequency scaling (DVFS) and clock gating (CG) which cause the processor to operate in various performance and power states depending on runtime workload characteristics. A voltage regulator (VR), which is designed to provide power to the processor at its highest performance level, can significantly degrade in efficiency when the processor operates in the deep power saving states. In this paper, we propose VR optimization techniques to improve the energy efficiency of the processor + VR system by using the workload dependent P- and C-state residency of real processors. Our experimental results for static VR optimization show up to 19%, 20%, and 4% reduction in energy consumption for workstation, mobile and server multi-core processors. We also investigate the effect of dynamically changing VR parameters on the energy efficiency compared to the static optimization.