The soaring clocking frequency and integration density demand robust and stable power delivery to support tens of millions of transistor switching. In this paper, we consider the problem of minimizing the area of wires and decoupling capacitors (decaps) for a power delivery network, subject to the limit on integral of voltage drops. First, we derive the gradients of constraint function without Tellegen's theorem. This greatly simplifies the discuss of adjoint sensitivity analysis. Then, we apply the IEKS method to speed up the sensitivity analysis over 3 times. Finally, this efficient analyzer is incorporated with the state-of-the-art nonlinear programming package, SNOPT, to perform the optimization. Extensive experimental results show that the proposed method can work efficiently for large power delivery networks.