I'm exploring optimization in RShiny and have produced the following example based on another example I found:

library(shiny)
#library(optimx)


fr <- function(x) {   
   x1 <- x[1]
   x2 <- x[2]
   2*(x[1]-1)^2   5*(x[2]-3)^2   3 
  # 100 * (x2 - x1 * x1)^2   (1 - x1)^2
  #x*x
}




ui <- fluidPage(
  titlePanel("Values"),
  
  sidebarLayout(
    sidebarPanel(
      sliderInput("range", 
                  label = "Choose two Values:",
                  min = -5, max = 5, value = c(-5, 5))
      
    ),
    mainPanel(
      textOutput("optim_out"),
      textOutput("optim_out_b")
    )
  )
)

# Define server logic required to draw a histogram
server <- function(input, output) {
  out <- reactive(optim(c(input$range[1], input$range[2]), fr))
  output$optim_out_b <- renderText(paste0("Par: ", out()$par[1], ", ", out()$par[2], " Value: ", out()$value, " Convergance: ", out()$convergence))
}

# Run the application 
shinyApp(ui = ui, server = server)

When the code is run, x1 turns out to be 1 and x2 is 3. My question is can I optimize the formula in function in a way that I can set the formula equal to a value, and then optimize. For example, is there a way to do:

2*(x[1]-1)^2   5*(x[2]-3)^2   3 = 172

And have the function optimized so that the values x1 and x2 are spit out with values that produce either 172 or the number closest to 172 as possible?

I tired just adding the = 172 to my function and it didn't work, that's just an example of what i'd like to do.

CodePudding user response：

1. Even though you intend to use shiny the question itself has nothing to do with it and shiny should be left out of the question and should not be a tag to satisfy the requirement that questions be minimal. Also optimx is not used in the question but appears in a library statement.

2. With two variables and one equation there won't be a unique solution but if you want any solution try minimizing the squared difference between fr and 172. Different starting values may produce different solutions.

Code--

optim(c(1, 1), function(x) (fr(x) - 172)^2)

giving:

$par
[1]  4.025171 -2.489776

$value
[1] 7.184557e-05

$counts
function gradient 
      49       NA 

$convergence
[1] 0

$message
NULL