Maximum instantaneous power in VLSI circuits has a great impact on circuit's reliability and the design of power and ground lines. To synthesizehighlyreliablesystems,accurateestimatesof maximumpower must be obtainedin various design phases. Unfortunately, determining the input patterns to induce the maximum current power is essentially a combinatorialoptimization problem. Even for circuits with small number of primary inputs PI's, it is CPU time intensive to conduct exhaustive search in the input vector space. The only feasible way is to nd good upper and lower bounds of the maximum power, and to make the gap between these two bounds as narrow as possible. In this paper, we present a continuous optimization approach to e ciently generate tight lower bounds of the maximum instantaneouspowerfor CMOS circuits. In our approach,each primary input PI of the circuit is allowed to assume any real number