The NOP-2 modeling language for nonlinear programming

This paper defines the modeling language NOP-2 for specifying general optimization problems, including constrained local or global nonlinear programs and constrained single and multistage programs. The proposed language is specifically designed to represent the internal (separable and repetitive) structure of the problem. Thus, it enables the model builder to somewhat abstract from the pure meaning of the problem in order to write it in a form that is more adapted to global and large scale optimization algorithms such as MINOS and GLOPT that is currently under development in our research group. Solving global optimization problems effectively in a rigorous way requires a lot of analytical knowledge about the functions involved. The speed of a branch-and-bound approach is, e.g., directly correlated to the amount of overestimation produced by interval enclosures or linear, quadratic, or convex relaxations.