On 19-Sep-05 Colin Badenhorst wrote: > Hi List, > > I've noticed that the latest version of my estimation software > now stores the Lagrange multiplier (parameter) for each estimated > block in my model. I was wondering if anyone had any thoughts on > how I could use this variable in some practical sense to further > interpret or validate my estimates. Unfortunately, my understanding > of the Lagrange multiplier has always been poor, so I'm not sure > exactly what it means.
In a constrained optimisation problem, e.g. minimising a function y(x, y, ...) with constraints expressed in the form g(x, y, ...) = c the value of the Lagrange multiplier associated with constraint g(x, y, ...) = c can be interpreted as the rate of change of the optimum value of f(x, y, ... ) with respect to change in c. Otherwise put, if say c1, c2, ... are the values of the constraint functions, the minimisation of f(x, y, ... ) will lead to a particular value of f() which will depend on the values of c1, c2, ... which were used, so it is a function fmin(c1, c2, ... ) of these. If U1, U2, ... are the Lagrange multipliers in the Lagrangean formulation of the problem, then U1 = dfmin(c1, c2, ... )/dc1 and similarly for U2 etc. Does this help? Best wishes, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 19-Sep-05 Time: 12:33:34 ------------------------------ XFMail ------------------------------
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