Hock Schittkowski Problem No 116 nco filter AMPL short 0 integer, := 13; set I := 1 .. N; var x {i in I} >= 0; param a > 0; param b > 0; param c > 0; param d > 0; param e > 0; param f > 0; minimize Obj: x[11] + x[12] + x[13]; s.t. c1: x[3] - x[2] >= 0; s.t. c2: x[2] - x[1] >= 0; s.t. c3: 1 - a * x[7] + a * x[8] >= 0; s.t. c4: x[11] + x[12] + x[13] >= 50; s.t. c5: x[13] - b * x[10] + c * x[3] * x[10] >= 0; s.t. c6: x[5] - d * x[2] - e * x[2] * x[5] + f * x[2]^2 >= 0; s.t. c7: x[6] - d * x[3] - e * x[3] * x[6] + f * x[3]^2 >= 0; s.t. c8: x[4] - d * x[1] - e * x[1] * x[4] + f * x[1]^2 >= 0; s.t. c9: x[12] - b * x[9] + c * x[2] * x[9] >= 0; s.t. c10: x[11] - b * x[8] + c * x[1] * x[8] >= 0; s.t. c11: x[5] * x[7] - x[1] * x[8] - x[4] * x[7] + x[4] * x[8] >= 0; s.t. c12: 1 - a * (x[2] * x[9] + x[5] * x[8] - x[1] * x[8] - x[6] * x[9]) - x[5] - x[6] >= 0; s.t. c13: x[2] * x[9] - x[3] * x[10] - x[6] * x[9] - 500 * x[2] + 500 * x[6] + x[2] * x[10] >= 0; s.t. c14: x[2] - 0.9 - a * (x[2] * x[10] - x[3] * x[10]) >= 0; s.t. c15: x[11] + x[12] + x[13] <= 250; s.t. b1: 0.1 <= x[1] <= 1; s.t. b2: 0.1 <= x[2] <= 1; s.t. b3: 0.1 <= x[3] <= 1; s.t. b4: 0.0001 <= x[4] <= 0.1; s.t. b5: 0.1 <= x[5] <= 0.9; s.t. b6: 0.1 <= x[6] <= 0.9; s.t. b7: 0.1 <= x[7] <= 1000; s.t. b8: 0.1 <= x[8] <= 1000; s.t. b9: 500 <= x[9] <= 1000; s.t. b10: 0.1 <= x[10] <= 500; s.t. b11: 1 <= x[11] <= 150; s.t. b12: 0.0001 <= x[12] <= 150; s.t. b13: 0.0001 <= x[13] <= 150; ]]> data; param a := 0.002; param b := 1.262626; param c := 1.231059; param d := 0.03475; param e := 0.975; param f := 0.00975; var x := 1 0.5 2 0.8 3 0.9 4 0.1 5 0.14 6 0.5 7 489 8 80 9 650 10 450 11 150 12 150 13 150; solve; display _varname, _var; FILTER-AMPL sample submission