1. Kennedy & Howroyd (1956) have discussed the application of the Lagrangian multiplier technique to actuarial problems. This technique permits the analytical solution of constrained optimization problems, where both the function to be optimized and the constraints must satisfy stringent analytical conditions. In particular, the first derivatives of all functions must exist.

When constraints comprise inequality as well as equation restrictions, as is the case in linear and non-linear programming, then the conditions required for the Lagrangian multiplier technique do not hold. It was therefore found necessary to develop a new body of techniques, known as mathematical programming techniques, for the solution of constrained optimization problems involving inequality constraints.