Improving solver success in reaching feasibility for sets of nonlinear constraints

Whether a given nonlinear solver can reach a feasible point for a set of nonlinear constraints depends heavily on the initial point provided. We develop a range of computationally cheap constraint consensus algorithms that move from a given initial point to a better final point that is then passed to the nonlinear solver. Empirical tests show that this added step greatly improves the success rate of various nonlinear solvers in reaching feasibility, and reduces the effort they expend in doing so. We also develop a new initial point placement heuristic for use when an initial point is not provided by the modeller. Empirical tests show much improved performance for this new heuristic, both alone and in conjunction with the constraint consensus algorithms.