A Continuation Method for Nonlinear Regression

Many iterative regression methods only perform well near a solution. One may construct a modified problem with a free parameter $(k)$, which has a known solution for a particular k. By suitably deforming this problem through k-space one may, always remaining close to an intermediate solution, eventually solve the original problem. The continuation method was used to perform three nonlinear least squares regressions where the conventional Newton methods failed to converge. In particular, the third problem was associated with experimental kinetic data and differential equations which needed to be integrated numerically. No satisfactory answers were obtainable from the Gauss–Newton method, while the continuation (parameter variation) method showed its robustness by converging for a large range of initial values.