library(tidyverse)
library(plotly)
#library(NlcOptim)
#library(Rsolnp)

## define set curve function ----
outerSolve <- function(x, a){

  a[1] * (1 - innerSolve(x, a) * (x - 1))

}

# part of the curve function
innerSolve <- function(x, a){

  a[2] * x ^ a[3]

}

# check if constraint is fulfilled
checkConstraint <- function(a){

  if(Vcon[2] / (1 - innerSolve(xcon[2], a) * (xcon[2] - 1)) <=
     Vcon[1] / (1 - innerSolve(xcon[1], a) * (xcon[1] - 1))) {

    return(TRUE)

  } else {

    return(FALSE)
  }


}

# create sample data
sampleData <- (function(){

  # set x range
  x = seq(50, 800, 5)

  # set coefficents
  setCoef <- c(80, 0.004, -0.3)

  # calculate y with some noise and create dataframe
  set.seed(123)
  tmpDF <- tibble(
    x = x,
    y = outerSolve(x, setCoef) + rnorm(length(x), 0, 0.02)
         )

  p <- plot_ly(x = ~ x, y = ~ y, data = tmpDF, type = 'scatter', mode = 'markers')

  return(list(setCoef = setCoef, raw = tmpDF, plot = p))

})()

# start values for target coefficents
startCoef <- c(max(sampleData$raw$y), 0.0001, -0.1)

# curve fitting with nls
refCurveFitting <- (function(){

  tmpModel = nls(
  y ~ outerSolve(x, c(find.a1, find.a2, find.a3)),
  data = sampleData$raw,
  start = c(
    find.a1 = startCoef[1],
    find.a2 = startCoef[2],
    find.a3 = startCoef[3]
  ),
  trace = TRUE,
  control = nls.control(maxiter = 100)
)

return(list(model = tmpModel, gof = tibble(AIC = AIC(refCurveFitting$model),
                                       BIC = BIC(refCurveFitting$model))
            )
       )

})()

# set constraint values
Vcon <- c(150, 130)
xcon <- c(50, 300)

checkConstraint(sampleData$setCoef)
[1] FALSE

minFunction <- function(a){
sampleData$raw %>%
      mutate(predicted.y = outerSolve(x, a),
             squaredRes = (y - predicted.y) ^ 2
      ) %>%
      summarise(sum.squaredRes = sum(squaredRes)) %>%
      pull(sum.squaredRes)
}