Finding Good Starting Points for Solving Structured and Unstructured Nonlinear Constrained Optimization Problems

In this paper, we develop heuristics for finding good starting points when solving large-scale nonlinear constrained optimization problems (COPs). We focus on nonlinear programming (NLP) and mixed-integer NLP (MINLP) problems with nonlinear non-convex objective and constraint functions. By exploiting the highly structured constraints in these problems, we first solve one or more simplified versions of the original COP, before generalizing the solutions found by interpolation or extrapolation to a good starting point. In our experimental evaluations of 190 NLP (resp., 52 MINLP) benchmark problems, our approach can solve 97.9% (resp., 71.2%) of the problems using significantly less iterations from our proposed starting points, as compared to 85.3% (resp., 46.2%) of the problems solvable by the best existing solvers from their default starting points.