Function minimization with equality constraints in

问题:

When using constraints with simple equality in Mathematica 8, minimization doesn't work. E.g.

FindMinimum[{x^2 + y^2,  y == 1}, {x, y}]

works ok in Mathematica 6, but gives errors in version 8. Can anyone else confirm (or explain) this? Looks like fixing one of the parameters with a constraint confuses version 8. Putting xy==1 is OK, also any inequality.

Any simple workaround on this? I have tried changing the Method, no luck. I would like to keep all the parameters in the parameter list, but hold some of them with simple constraint instead of removing the parameter name from the list. I have a working code in version 6, which does not work anymore in 8.

回答1:

Your syntax appears to be incorrect:

FindMinimum[{x^2 + y^2,  y == 1}, {x, y}]

which asks to start x with a value of y. This doesn't make much sense to me.

Perhaps you are attempting to do:

Minimize[{x^2 + y^2, y == 1}, {x, y}]

  Out:  {1, {x -> 0, y -> 1}}

---

Apparently your syntax is valid. Consider Minimize as shown above to be a possible work-around for your problem.

回答2:

Another workaround would be to use version 9.

In[1]:= FindMinimum[{x^2 + y^2, y == 1}, {x, y}]
Out[1]= {1., {x -> 0., y -> 1.}}

Which is to say, what you show above is a bug that has kindly fixed itself for a future release.

Daniel Lichtblau Wolfram Research

回答3:

In[31]:= NMinimize[{x^2 + y^2, y == 1}, {x, y}]

Out[31]= {1., {x -> -3.20865*10^-9, y -> 1.}}

In[32]:= FindMinimum[{x^2 + y^2, 1 - 10^-10 <= y <= 1 + 10^-10}, {x, y}]

Out[32]= {1., {x -> 0., y -> 1.}}

However, I wonder how to force mma to keep on searching even if it encounters a infinite expression? Can anybody share your idea?

thanks ^_^