Fast and effective gate-sizing with multiple-Vt assignment using generalized Lagrangian relaxation

Simultaneous gate-sizing with multiple V_t assignment for delay and power optimization is a complicated task in modern custom designs. In this work, we make the key contribution of a novel gate-sizing and multi-V_t assignment technique based on generalized Lagrangian relaxation. Experimental results show that our technique exhibits linear runtime and memory usage, and can effectively tune circuits with over 15,000 variables and 8,000 constraints in under 8 minutes (250× faster than state-of-the-art optimization solvers).