The emergence of power as a first-class design constraint has fueled the proposal of a growing number of run-time power optimizations. Many of these optimizations trade-off power saving opportunity for a variable performance loss which depends on application characteristics and program phase. Furthermore, the potential benefits of these optimizations are sometimes non-additive, and it can be difficult to identify which combinations of these optimizations to apply. Trial-and-error approaches have been proposed to adaptively tune a processor. However, in a chip multiprocessor, the cost of individually configuring each core under a wide range of optimizations would be prohibitive under simple trial-and-error approaches. In this work, we introduce an adaptive, multi-optimization power saving strategy for multi-core power management. Specifically, we solve the problem of meeting a global chip-wide power budget through run-time adaptation of highly configurable processor cores. Our approach applies analytic modeling to reduce exploration time and decrease the reliance on trial-and-error methods. We also introduce risk evaluation to balance the benefit of various power saving optimizations versus the potential performance loss. Overall, we find that our approach can significantly reduce processor power consumption compared to alternative optimization strategies.