(216d) Why Doesn't My NLP Converge? – Debugging Nonlinear Programs with an Intermediate Callback

Nonlinear optimization is a powerful decision-support tool in chemical engineering and a critical component of many process control algorithms. However, while nonlinear local optimization algorithms have global convergence proofs, solvers can fail to converge in practice for a variety of reasons including poor conditioning, degeneracy, cycling, and local infeasibility. In such cases, the reasons for non-convergence can be difficult to identify, especially if a higher level algebraic modeling environment such as AMPL, GAMS, Pyomo, or JuMP is used to communicate with the solver and if the solver’s internal data structures are not available in the user’s programming environment. Tighter integration of the modeling language and solver can help identify causes of failure by allowing investigation of a solver’s internal data structures with potentially model-specific debugging routines. In particular, the intermediate callback provided by the nonlinear optimization solver Ipopt can be used to investigate the primal-dual iterates and infeasibilities during the iterations of a solve. If derivative information of the optimization problem is available, Jacobian and Hessian matrices may be investigated as well. In a full-featured programming language like Python or Julia, linear algebra and graph theory packages are available, allowing sophisticated analysis of the state of the optimization problem at every iteration.