How to solve nonlinear equations in R with Controls

Question

I try to solve nonlinear equations with controls.

Here is my code:

fun <- function(x) {

  b0 <- (0.64*1+(1-0.64)*x[1]*(x[2]*x[1]-1)+x[1]*1*(1-x[2])*x[3])/(x[1]-1) -1805*2.85*0.64
  b1plus <-  (0.64*1+(1-0.64)*x[1]*(x[2]*x[1]-1.01)+x[1]*1.01*(1-x[2])*x[3])/(1.01*(x[1]-1)) -1805*2.85*0.64*(1+0.00235)
  b1minus <-  (0.64*1+(1-0.64)*x[1]*(x[2]*x[1]-0.99)+x[1]*0.99*(1-x[2])*x[3])/(0.99*(x[1]-1)) -1805*2.85*0.64*(1-0.00235)

  return(c(b0,b1plus,b1minus))
} 


multiroot(fun,c(1.5, 0, 0))

However, the result I get is far beyond the actual results. I wish to control x1 to the range (1.5,4), x2(0,1), x3(0,10000). How can I do that?

Thank you!!

Answer 1

Methods like 'Newton-Raphson' in multiroot or nleqslv do not work well together with bounds constraints. One possible approach is to square and sum the components of your function

fun1 <- function(x) sum(fun(x)^2)

and then treat this as a global optimization problem where you hope for a minimum value of 0.0 . For example, GenSA provides an implementation of "simulated annealing" that works reasonably well in low dimensions.

library(GenSA)
res <- GenSA(par=NULL, fn=fun1,
             lower=c(1.5,0,0), upper=c(4,1,10000),
             control=list(maxit=10e5))
res$value; res$par
## [1] 119.7869
## [1]    4.00    0.00 2469.44

Several tries did not find a lower function value than this one, which makes me think there is no common root in the constraint box you requested.