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NLA stands for nonlinear-algebraic. An NLA solver is one that can solve a system of nonlinear algebraic equations, possibly with constraints. Such systems, if well-defined, have only (at most) one solution, which depending on the structure of the system of equations may be determined by direct solution (or subsitution) of values, or possibly by iteration if there are 'blocks' of simultaneous equations.
The primary NLA solver for ASCEND is QRSlv and this solver is recommended for most problems.