# Extended Rosenbrock Function, n = 2
BEGIN
x1 = -1.2
x2 = 1
f1 = 10 * (x2 - x1^2)
f2 = 1 - x1
ff = f1^2 + f2^2
END
FMin(ff, x1, x2)


# Extended Rosenbrock Function, n = 4
BEGIN
x1 = -1.2
x2 = 1
x3 = -1.2
x4 = 1
f1 = 10 * (x2 - x1^2)
f2 = 1 - x1
f3 = 10 * (x4 - x3^2)
f4 = 1 - x3

ff = f1^2 + f2^2 + f3^2 + f4^2
END
FMin(ff, x1, x2, x3, x4)


# Extended Rosenbrock Function, n = 6
BEGIN
x1 = -1.2
x2 = 1
x3 = -1.2
x4 = 1
x5 = -1.2
x6 = 1
f1 = 10 * (x2 - x1^2)
f2 = 1 - x1
f3 = 10 * (x4 - x3^2)
f4 = 1 - x3
f5 = 10 * (x6 - x5^2)
f6 = 1 - x5

ff = f1^2 + f2^2 + f3^2 + f4^2 + f5^2 + f6^2
gg = -ff
END
FMin(ff, x1, x2, x3, x4, x5, x6)


# Extended Powell Singular Function, n = 4
BEGIN
x1 = 3
x2 = -1
x3 = 0
x4 = 1
f1 = x1 + 10 * x2
f2 = sqrt(5) * (x3 - x4)
f3 = (x2 - 2 * x3)^2
f4 = sqrt(10) * (x1 - x4)^2
ff = f1^2 + f2^2 + f3^2 + f4^2
END
FMin(ff, x1, x2, x3, x4)


# Extended Powell Singular Function, n = 8
BEGIN
x1 = 3
x2 = -1
x3 = 0
x4 = 1
x5 = 3
x6 = -1
x7 = 0
x8 = 1
f1 = x1 + 10 * x2
f2 = sqrt(5) * (x3 - x4)
f3 = (x2 - 2 * x3)^2
f4 = sqrt(10) * (x1 - x4)^2
f5 = x5 + 10 * x6
f6 = sqrt(5) * (x7 - x8)
f7 = (x6 - 2 * x7)^2
f8 = sqrt(10) * (x5 - x8)^2
ff = f1^2 + f2^2 + f3^2 + f4^2 + f5^2 + f6^2 + f7^2 + f8^2
END
FMin(ff, x1, x2, x3, x4, x5, x6, x7, x8)


# Trigonometric Function, n = 2
BEGIN
n = 2
x1 = 1 / n
x2 = 1 / n
f1 = n - (cos(x1) + (1) * (1 - cos(x1)) - sin(x1)) \
       - (cos(x2) + (1) * (1 - cos(x1)) - sin(x1))
f2 = n - (cos(x1) + (2) * (1 - cos(x2)) - sin(x2)) \
       - (cos(x2) + (2) * (1 - cos(x2)) - sin(x2))
ff = f1^2 + f2^2
END
FMin(ff, x1, x2)

# Trigonometric Function, n = 4 (???)
BEGIN
n = 4
x1 = 1 / n
x2 = 1 / n
x3 = 1 / n
x4 = 1 / n
f1 = n - (cos(x1) + (1) * (1 - cos(x1)) - sin(x1)) \
       - (cos(x2) + (1) * (1 - cos(x1)) - sin(x1)) \
       - (cos(x3) + (1) * (1 - cos(x1)) - sin(x1)) \
       - (cos(x4) + (1) * (1 - cos(x1)) - sin(x1))
f2 = n - (cos(x1) + (2) * (1 - cos(x2)) - sin(x2)) \
       - (cos(x2) + (2) * (1 - cos(x2)) - sin(x2)) \
       - (cos(x3) + (2) * (1 - cos(x2)) - sin(x2)) \
       - (cos(x4) + (2) * (1 - cos(x2)) - sin(x2))
f3 = n - (cos(x1) + (3) * (1 - cos(x3)) - sin(x3)) \
       - (cos(x2) + (3) * (1 - cos(x3)) - sin(x3)) \
       - (cos(x3) + (3) * (1 - cos(x3)) - sin(x3)) \
       - (cos(x4) + (3) * (1 - cos(x3)) - sin(x3))
f4 = n - (cos(x1) + (4) * (1 - cos(x4)) - sin(x4)) \
       - (cos(x2) + (4) * (1 - cos(x4)) - sin(x4)) \
       - (cos(x3) + (4) * (1 - cos(x4)) - sin(x4)) \
       - (cos(x4) + (4) * (1 - cos(x4)) - sin(x4))
ff = f1^2 + f2^2 + f3^2 + f4^2
END
FMin(ff, x1, x2, x3, x4)


# Helical Valley Function 
BEGIN
x1 = -1
x2 = 0
x3 = 0
z = 2 * pi() rad
y =  atan2(x2, x1) / z
f1 = 10 * (x3 - 10 * y )
f2 = 10 * (sqrt(x1^2 + x2^2) - 1)
f3 = x3
ff = f1^2 + f2^2 + f3^2
END
FMin(ff, x1, x2, x3)


# Wood Function 
BEGIN
x1 = -3
x2 = -1
x3 = -3
x4 = -1
ff = 100 * (x1^2 - x2)^2 + (1 - x1)^2 \
    + 90 * (x3^2 - x4)^2 + (1 - x3)^2 \
    + 10.1 * ((1 - x2)^2 + (1 - x4)^2) \
    + 19.8 * (1 - x2) * (1 - x4)
END
FMin(ff, x1, x2, x3,x4)