# Ref.: W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming # Codes. Lecture Notes in Economics and Mathematical Systems, v. 187, # Springer-Verlag, New York, 1981, p. 118. Model hs109 Parameters a = 50.176 b1= .25 b = sin(b1) c = cos(b1) l[1:2] = 0 l[3:4] = -0.55 l[5:7] = 196 l[8:9] = -400 u[1:2] = 1e20 u[3:4] = 0.55 u[5:7] = 252 u[8:9] = 800 End Parameters Variables x[1:9] = 0, >=l[1:9], <=u[1:9] ! optimal solution ??? ! x[1] = 674.8881, >=l[1], <=u[1] ! x[2] = 1134.170, >=l[2], <=u[2] ! x[3] = 0.1335691, >=l[3], <=u[3] ! x[4] = -0.3711526, >=l[4], <=u[4] ! x[5] = 252, >=l[5], <=u[5] ! x[6] = 252, >=l[6], <=u[6] ! x[7] = 201.465, >=l[7], <=u[7] ! x[8] = 426.661, >=l[8], <=u[8] ! x[9] = 368.494 , >=l[9], <=u[9] obj End Variables Equations x[4] - x[3] + .55 >= 0 x[3] - x[4] + .55 >= 0 2250000 - x[1]^2 - x[8]^2 >= 0 2250000 - x[2]^2 - x[9]^2 >= 0 x[5] * x[6] * sin(-x[3] - .25) + x[5] * x[7] * sin(-x[4] - .25) + & 2 * b * x[5]^2 - a * x[1] + 400 * a = 0 x[5] * x[6] * sin(x[3] - .25) + x[6] * x[7] * sin(x[3] - x[4] - .25) + & 2 * b * x[6]^2 - a * x[2] + 400 * a = 0 x[5] * x[7] * sin(x[4] - .25) + x[6] * x[7] * sin(x[4] - x[3] - .25) + & 2 * b * x[7]^2 + 881.779 * a = 0 a * x[8] + x[5] * x[6] * cos(-x[3] - .25) + & x[5] * x[7] * cos(-x[4] - .25) - 200 * a - 2 * c * x[5]^2 + & .7533e-3 * a * x[5]^2 = 0 a * x[9] + x[5] * x[6] * cos(x[3] - .25) + & x[6] * x[7] * cos(x[3] - x[4] - .25) - 2 * c * x[6]^2 + & .7533e-3 * a * x[6]^2 - 200 * a = 0 x[5] * x[7] * cos(x[4] - .25) + x[6] * x[7] * cos(x[4] - x[3] - .25) - & 2 * c * x[7]^2 + 22.938 * a + .7533e-3 * a * x[7] ^2 = 0 x[1:2] >= 0 -.55 <= x[3:4] <= .55 196 <= x[5:7] <= 252 -400 <= x[8:9] <= 800 ! best known objective = 5362.06928 obj = 3 * x[1] + 1e-6 * x[1]^3 + 2 * x[2] + .522074e-6 * x[2]^3 End Equations End Model