In this paper, we present an efficient method to budget on-chip decoupling capacitors (decaps) to optimize power delivery networks in an area efficient way. Our algorithm is based on an efficient gradient-based non-linear programming method for searching the solution. Our contributions are an efficient gradient computation method (time-domain merged adjoint network method) and a novel equivalent circuit modeling technique to speed up the optimization process. Experimental results demonstrate that the algorithm is capable of efficiently optimizing very large scale P/G networks.