Constrained nonlinear systems (CNS)

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Mathematically, a constrained nonlinear system (CNS) model looks like:

find

subject to

F(x) = 0

L < x < U

G(x) < b

where

x is a set of variables

F is a set of nonlinear equations.

In addition the number of equations and the number of unknown variables x need to be of equal dimension and the variables x are continuous.

The (possibly empty) constraints L < x < U are not intended to be binding at the solution, but instead are included to constrain the solution to a particular domain or to avoid regions where F(x) is undefined. The (possibly empty) constraints G(x) < b are intended for the same purpose.

The CNS model is a generalization of a problem form involving solve for x over a system of equations with one equation present for each x (a square system) like F(x) = 0. There are a number of advantages to using the CNS model type (compared to solving as an NLP with a dummy objective, say), including:

•	A check by GAMS that the model is really square,

•	Solution/model diagnostics are generated by the solver (e.g. singular at solution, locally unique solution), and

•	A potential reduction in solution times, by taking better advantage of the model properties.

For information on the names of the solvers that can be used on the CNS problem class see the section on Solver Model type Capabilities.