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A unified optimization framework is presented for simultaneous gate sizing and placement. These processes are unified using Lagrangian multipliers, which synchronize the efforts of the gate sizing and placement subproblems. As far as we know, this is the first work that formulates and solves the simultaneous gate sizing and placement under area density constraints, which are handled by the quadratic penalty method. We show that this rigorous framework results in an algorithm that is faster than separate iterations of gate sizing and placement steps, and leads to more robust results for a set of benchmarks.