[SciPy-user] Solving an equation using scipy.optimize.newton
Wed Sep 5 20:57:41 CDT 2007
Thanks Dominique and dmitrey,
Dominique Orban wrote:
> On 9/5/07, *email@example.com <mailto:firstname.lastname@example.org>*
> <email@example.com <mailto:firstname.lastname@example.org>> wrote:
> Hi all,
> I'm trying to solve an equation f(x) = 0 with scipy.optimize.newton .
> However the problem isn't so simple. There are bound constraints for my
> equation: the equation cannot be evaluated when x is out of [Min,
> Max], but
> the root is always in the interval of [Min, Max]
> When newton() iterates to find a root, it sometimes try to evaluate the
> equation with a x out of [Min, Max], and then error occurs.
> How to solve this problem ?
> I couldn't easily find two points with different signs every time,
> so methods
> like brentq don't work here.
> There are variants of Newton's method that can handle bound constraints.
> However, another way to treat your problem would be to solve the
> optimization problem:
Are there any trust region optimization method with python interface ?
> minimize 0
> subject to f(x) = 0, and Min <= x <= Max.
> The objective function of this problem is constant, so any x satisfying
> the constraints is optimal, and is what you are looking for. Note
> however that you now have an optimization problem with nonlinear
> equality constraints.
> If a solver isn't able to identify a point satisfying the constraints,
> it will usually guarantee some sort of 'proximity property', i.e., the
> final iterate will minimize the residual of constraints in some sense.
I can transform my problem to a bound constrained optimization problem,
but I still have to find an optimization solver who only evaluate my
equation in trust region([Min, Max]). Will lbfgsb or tnc meet the
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