Enabling Efficient Analog Synthesis by Coupling Sparse Regression and Polynomial Optimization

Abstract

The challenge of equation-based analog synthesis comes from its dual nature: functions producing good least-square fits to SPICE-generated data are non-convex, hence not amenable to efficient optimization. In this paper, we leverage recent progress on Semidefinite Programming (SDP) relaxations of polynomial (non-convex) optimization. Using a general polynomial allows for much more accurate fitting of SPICE data compared to the more restricted functional forms. Recent SDP techniques for convex relaxations of polynomial optimizations are powerful but alone still insufficient: even for small problems, the resulting relaxations are prohibitively high dimensional.We harness these new polynomial tools and realize their promise by introducing a novel regression technique that fits non-convex polynomials with a special sparsity structure. We show that the coupled sparse fitting and optimization (CSFO) flow that we introduce allows us to find accurate high-order polynomials while keeping the resulting optimization tractable.Using established circuits for optimization experiments, we demonstrate that by handling higher-order polynomials we reduce fitting error to 3.6% from 10%, on average. This translates into a dramatic increase in the rate of constraint satisfaction: for a 1% violation threshold, the success rate is increased from 0% to 78%.