Minimization - optimization alg. or equation alg.?

  • Thread starter sodemus
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Hello everybody!
I guess my question is mainly concerned with numerical algorithms...
Given a problem of the form
min w = f(x)
subject to
g1(x)=0
:
:
gn(x)=0
where x is a m x 1 vector, n < m.

From a numerical standpoint, how can I know whether it is preferably to solve it by setting up the Lagrangian and solve the resulting system of m + n non linear equations with appropriate algorithms OR to implement an appropriate algorithm to solve the minimization problem directly? As far as my particular problem goes, let's say n = 2 and m = 25.

Any help is more than appreciated!
 

fresh_42

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If you had knowledge about the constraints, e.g. linearity, you could chose another approach. Without any further information, Lagrange multipliers should be fine.
 

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