Examples for 'nloptr::nloptr-package'

### ** Examples


# Example problem, number 71 from the Hock-Schittkowsky test suite.
#
# \min_{x} x1*x4*(x1 + x2 + x3) + x3
# s.t.
#    x1*x2*x3*x4 >= 25
#    x1^2 + x2^2 + x3^2 + x4^2 = 40
#    1 <= x1,x2,x3,x4 <= 5
#
# we re-write the inequality as
#   25 - x1*x2*x3*x4 <= 0
#
# and the equality as
#   x1^2 + x2^2 + x3^2 + x4^2 - 40 = 0
#
# x0 = (1,5,5,1)
#
# optimal solution = (1.00000000, 4.74299963, 3.82114998, 1.37940829)


library('nloptr')

#
# f(x) = x1*x4*(x1 + x2 + x3) + x3
#
eval_f <- function( x ) {
    return( list( "objective" = x[1]*x[4]*(x[1] + x[2] + x[3]) + x[3],
                  "gradient" = c( x[1] * x[4] + x[4] * (x[1] + x[2] + x[3]),
                                  x[1] * x[4],
                                  x[1] * x[4] + 1.0,
                                  x[1] * (x[1] + x[2] + x[3]) ) ) )
}

# constraint functions
# inequalities
eval_g_ineq <- function( x ) {
    constr <- c( 25 - x[1] * x[2] * x[3] * x[4] )

    grad   <- c( -x[2]*x[3]*x[4],
                 -x[1]*x[3]*x[4],
                 -x[1]*x[2]*x[4],
                 -x[1]*x[2]*x[3] )
    return( list( "constraints"=constr, "jacobian"=grad ) )
}

# equalities
eval_g_eq <- function( x ) {
    constr <- c( x[1]^2 + x[2]^2 + x[3]^2 + x[4]^2 - 40 )

    grad   <- c(  2.0*x[1],
                  2.0*x[2],
                  2.0*x[3],
                  2.0*x[4] )
    return( list( "constraints"=constr, "jacobian"=grad ) )
}

# initial values
x0 <- c( 1, 5, 5, 1 )

# lower and upper bounds of control
lb <- c( 1, 1, 1, 1 )
ub <- c( 5, 5, 5, 5 )


local_opts <- list( "algorithm" = "NLOPT_LD_MMA",
                    "xtol_rel"  = 1.0e-7 )
opts <- list( "algorithm" = "NLOPT_LD_AUGLAG",
              "xtol_rel"  = 1.0e-7,
              "maxeval"   = 1000,
              "local_opts" = local_opts )

res <- nloptr( x0=x0,
               eval_f=eval_f,
               lb=lb,
               ub=ub,
               eval_g_ineq=eval_g_ineq,
               eval_g_eq=eval_g_eq,
               opts=opts)
print( res )