#Copyright (C) 2013-2015 Abdalkarim Awad
#if the package is not yet installed, uncomment the following 
#line to install the nonlinear optimization package
#install.packages("nloptr")
library('nloptr') #use the library
 
#objective function
#It is the sum of all costs of all generators 
#let PA=x1, PB=x2
#f(x)=399.8+11.69*x[1]+0.00334*x[1]^2+616.9+11.83*x[2]+0.00149*x[2]^2
function_f <- function(x){ 
return(399.8+11.69*x[1]+0.00334*x[1]^2+616.9+11.83*x[2]+0.00149*x[2]^2 )
}
# constraint function g(x),
#x1+x2=600 ==> x1+x2-600=0
#the optimization method COBYLA supports equality constraints 
#by transforming them into two inequality constraints.
#x1+x2-600=0 ==> x1+x2-600<=0 and x1+x2-600>=0
#==> x1+x2-600<=0  and -x1-x2+600<=0 
const_g<- function( x) {
    return(rbind(c(x[1]+x[2]-600), -c(+x[1]+x[2]-600)))
}

 
# Solve using NLOPT_LN_COBYLA 
results <- nloptr( x0=c(100,100), #initial values
	eval_f=function_f,  #min (f(x))	
	lb = c(0,0), #lower bound for x1 and x2
	ub = c(Inf,Inf), #upper bound for x1 and x2
	eval_g_ineq= const_g, #equality and inequality constraints
	opts = list("algorithm"="NLOPT_LN_COBYLA",xtol_rel = 1e-4)) #options
print( results )
min_value=results$objective
x=results$solution
PA=x[1]
PB=x[2]
min_value
PA
PB