Finding Good Starting Points for Solving Nonlinear Constrained Optimization Problems by Parallel Decomposition

In this paper, we develop heuristics for finding good starting points when solving large-scale nonlinear constrained optimization problems (COPS) formulated as nonlinear programming (NLP) and mixed-integer NLP (MINLP). By exploiting the localities of constraints, we first partition each problem by parallel decomposition into subproblems that are related by complicating constraints and complicating variables. We develop heuristics for finding good starting points that are critical for resolving the complicating constraints and variables. In our experimental evaluations of 255 benchmarks, our approach can solve 89.4% of the problems, whereas the best existing solvers can only solve 42.8%.