In the last week, I continue to work on the decap optimization.

1. I have considered the adjoint sensivity approach. However, from the experiment and theoretical study, the sensitivity of impedance on decaps heavily depends on the electrical environment around a location. Therefore, the sensitivity must be updated frequently with decap insertion. Therefore, the method is not so useful in this case.

2. Three heurestic approaches have been careful studied and compared. 
   a. Maximum suppression: Select location that suppresses maximum peak in the frequency band.
   b. Peak following suppression: select location suppress peaks from low frequency to high frequency. 
   c. Average suppression: select location that reduce the average amplitude in the frequency band. 

   Experiments have been conducted with a type of decap with 1pf, 0.2ph and 0.2ohm. Optimization finish in roughly 10min with 100 decaps inserted (~0.1nf). The results of a. and b. are very close to the optimal solution ( with all the ports connected to ground). c. is worse than a. and b.

   However, there are still problems to be solved: 
   a. The optimal impedance is still high. To solve, I will further consider on-chip decaps. Also I am working on the weight of each frequency so that I can justify the solution with different frequency components or time domain amplitude.
   b. The approach is hard to consider different types since in each step it is hard to justify which type is best for the final cost.

3. Now I am working on following mathematical approaches:
	1. Sequential linear programming. 
		a. In frequency domain: minimize the sum of impedance and cost.
		b. In time domain: use wighted sum of impedance to approximate the time domain response.