Subgradient Based Multiple-Starting-Point Algorithm for Non-Smooth Optimization of Analog Circuits

Wenlong Lv1, Fan Yang1,a, Changhao Yan1, Dian Zhou1,2 and Xuan Zeng1,b
1State Key Lab of ASIC & System, School of Microelectronics, Fudan University, Shanghai, P. R. China.
2Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX, U.S.A.


Starting from a set of starting points, the multiplestarting- point optimization searches the local optimums by gradient-guided local search. The global optimum is selected from these local optimums. The region-hit property of the multiple-starting-point optimization makes the multiple-startingpoint approach more likely to reach the global optimum. However, for non-smooth objective functions, e.g., worst-case optimization, the traditional gradient based local search methods may stuck at non-smooth points, even if the objective function is smooth ``almost everywhere''. In this paper, we propose a subgradient based multiple-starting-point algorithm for nonsmooth optimization of analog circuits. Subgradients instead of traditional gradients are used to guide the local search of the nonsmooth optimization. The Shor's R algorithm is used to accelerate the subgradient based local search. A two-stage optimization strategy is proposed to deal with the constraints in analog circuit optimization. Our experiments on 2 circuits show that the proposed method is very efficient for worst-case optimization. The proposed approach can achieve much better solutions with less simulations, compared with the traditional gradient based method, smoothing approximation method, smooth relaxation method and differential evolution algorithms.

Keywords: Worst-case optimization, Shor's R algorithm, Multiple-starting-point.

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