ARKI Consulting & Development A/S
The CONOPT Algorithm
CONOPT is a solver for large-scale nonlinear
optimization (NLP) developed and maintained by ARKI Consulting &
Development A/S in
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. However, new
2nd derivative-based methods have made these models much easier with
the new CONOPT version 3 than with our older CONOPT version 2.