ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 17 Sep 2012 07:01:13 +0200simple numerical solve (2-variables!!)https://ask.sagemath.org/question/9325/simple-numerical-solve-2-variables/Hello,
Thanks for the help, I'm trying to move from Mathematica to Sage, but I'm still having some trouble with the basics. Specifically, I'm moving from 1-var to 2-var numerical optimization/solver. I want to optimize function g or, equivalently, solve the system of first-order conditions, f. So far, I have not been able to get any of the scipy routines to work. Is there a simple way to do this? (Note: the objective function is concave wrt to both arguments.)
Thanks!
jv
#Constants
y_a = 50
y_b = 50
x = 40
alpha_a = .2
alpha_b = .2
#Functions
v(n)= n^.5
v1(n) = derivative(v(n),n)
u(n)= n^.5
u1(n) = derivative(u(n),n)
#Variables
var('g_a')
var('x_a')
#Optimization (over [0, x])
g = (v(g_a+alpha_b*(x-g_a))-u(y_a)+u(y_a-x_a))*(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))
f1 = ((1-alpha_b)*v1(g_a+alpha_b*(x - g_a)))/((1-alpha_a)*v1(x-g_a+alpha_a*(g_a)))==(v(g_a+alpha_b*(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))
f2 = (u1(x_a)/u1(x-x_a)) == (v(g_a+alpha_b*(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))
f(g_a, x_a) = (f1, f2)mattiasMon, 17 Sep 2012 07:01:13 +0200https://ask.sagemath.org/question/9325/