Cognitive radio network (CRN) is a promising approach to improve spectrum efficiency for wireless networking. This paper investigates how to perform optimal power control on each node (or per-node based power control) in the network so as to optimize network performance. Per-node based power control is a difficult problem due to its large design space (i.e., interaction among the powers on different nodes in the network) and the coupling relationship between power control and upper layers (scheduling and routing). In this paper, we develop a formal mathematical model for joint power control, scheduling, and routing. We formulate a cross-layer optimization problem encompassing these three layers and develop a unified solution procedure based on branch-and-bound framework and convex hull relaxation. Using numerical results, we demonstrate the efficacy of the solution procedure and offer insights on the behavior of per-node based power control.