Печать вывода функции R optim в R shiny

Вам нужно только использовать reactive на сервере, а затем вернуть текст с renderPrint или renderText. См. Пример:

library(shiny)

fr <- function(x) {   ## Rosenbrock Banana function
  x1 <- x[1]
  x2 <- x[2]
  100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}

# Define UI for application that draws a histogram
ui <- fluidPage(
  titlePanel("Sim Values"),

  sidebarLayout(
    sidebarPanel(
      sliderInput("range", 
                  label = "Initial values for the parameters to be optimized over:",
                  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$optim_out <- renderPrint(out())
   output$optim_out_b <- renderText(paste0("Par: ", out()$par[1], " ", out()$par[2], " Value: ", out()$value))
}

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