The CONOPT Algorithm

CONOPT is a solver for large-scale nonlinear optimization (NLP) originally developed and maintained by ARKI Consulting & Development A/S in Bagsvaerd, Denmark. CONOPT is a feasible path solver based on the old proven GRG method with many newer extensions. CONOPT has been designed to be efficient and reliable for a broad class of models. The original GRG method helps achieve reliability and speed for models with a large degree of nonlinearity, i.e. difficult models, and CONOPT is often preferable for very nonlinear models and for models where feasibility is difficult to achieve. Extensions to the GRG method such as preprocessing, a special phase 0, linear mode iterations, and a sequential linear programming and a sequential quadratic programming component makes CONOPT efficient on easier and mildly nonlinear models as well. The multi-method architecture of CONOPT combined with build-in logic for dynamic selection of the most appropriate method makes CONOPT a strong all-round NLP solver.

All components of CONOPT have been designed for large and sparse models. Models with over 10,000 constraints are routinely being solved. Specialized models with up to 1 million constraints have also been solved with CONOPT. The limiting factor is difficult to define. It is a combination of the number of constraints or variables with the number of super basic variables, a measure of the degrees of freedom around the optimal point. Models with over 500 super basic variables can sometimes be slow.