Provably all-convex optimal minimum-error convex fitting algorithm using linear programming

Convexity is a key property to global optimal for mathematical programming. Previous convex fitting works can only guarantee convexity at table entries or sampled points using semi-definite programming (SDP). In this work, we demonstrate that convexity can be guaranteed not only at listed tabular entries but also whole functional domain with minimum perturbation using simply linear programming (LP). Extensive experimental results of industrial cell library demonstrate that our method can reach global convexity 9X faster than the SDP approach. Its application on circuit tuning is also presented.