Nonlinear optimization (NLO) per definitionem covers a vast range of problems, from trivial to practically intractable. For this reason, it is impossible to offer "guaranteed" advice to NLO software users. This fact becomes especially obvious, when facing unusually hard and/or previously unexplored NLO challenges. In the present study we offer some related practical observations, propose a simple heuristic approach, and then suggest corresponding option settings for use with the Lipschitz Global Optimizer (LGO) solver suite. LGO serves for general – global and local – NLO. The LGO option settings proposed here are directly related to the "expectably sufficient" computational effort to handle a broad range of NLO problems. These option settings are then evaluated experimentally, by solving a collection of widely used NLO test problems which are based on various real-world optimization applications and academic challenges. We also include illustrative results for several well-known scalable optimization problems which are scientifically relevant and increasingly difficult as the size of the model-instances grows. Based on our computational test results, it is possible to offer careful guidance to LGO users, and – arguably, mutatis mutandis – to users of other NLO software products with a similarly broad mandate.
Author: J.D. Pinter, PCS Inc., Canada. Submitted for publication: June 2014.