Strengthening Convex Relaxations with Bound Tightening for Power Network Optimization

Convexification is a fundamental technique in mixed-integer nonlinear optimization and many convex relaxations are parametrized by variable bounds, i.e., the tighter the bounds, the stronger the relaxations. This paper studies how bound tightening can improve convex relaxations for power network optimization. It adapts traditional constraint-programming concepts e.g., minimal network and bound consistency to a relaxation framework and shows how bound tightening can dramatically improve power network optimization. In particular, the paper shows that the Quadratic Convex relaxation of power flows, enhanced by bound tightening, almost always outperforms the state-of-the-art Semi-Definite Programming relaxation on the optimal power flow problem.