It is to apply the langrange multiplier in two equation of curves to obtain maxima and minima. But applying in two set of equation is difficult for me. Can any one give a guidence?
In some text books this is also called the "Lagrange multiplier method". Look it up! It's not complicated, but not always applicable. (Without convexity of the original problem it will not work.)
We have applied the LMM for the problem of finding the distance between two quadrics (for instance, ellipses or ellipsoids). The method is based on the elimination of variable theory in nonlinear algebraic equation system and reduces the problem to that of solving a univariate equation.. Take a look at our recent paper "Metric Problems for Quadrics in Multidimensional Space". This is a purely analytical approach, and therefore is rather computationally expensive. However it works at least in space dimensions up to 4. If you need further details just drop me a message.
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