! Nonlinear electrical network ! The problem is corrected to conform to the problem as stated in ! D. M. Himmelblau, Applied Nonlinear Programming, ! McGraw-Hill, 1972, pp. 413-414 ! except that jump-discontinuities in the objective function are ! omitted by stating it as the sum of two piecewise-linear terms Model hs87 Parameters a = 131.078 b = 1.48477 ! Hock & Schittkowski say 1.48577 c = 0.90798 d0 = 1.47588 e0 = 1.47588 d = cos(d0) e = sin(e0) lim[1] = 300 lim[2] = 100 lim[3] = 200 rate[1] = 30 rate[2] = 31 rate[3] = 28 rate[4] = 29 rate[5] = 30 End Parameters Variables add[1:3] > 0 slk[1:3] x[1] = 390, >= 0, <= 400 x[2] = 1000, >= 0, <= 1000 x[3] = 419.5, >= 340, <= 420 x[4] = 340.5, >= 340, <= 420 x[5] = 198.175, >= -1000, <= 1000 ! Hock & Schittkowski say <= 10000 x[6] = 0.5, >= 0, <= 0.5236 obj[1:2] End Variables Equations ! piecewise linear add[1] = x[1] - lim[1] + slk[1] add[2] = x[2] - lim[2] + slk[2] add[3] = x[2] - lim[3] + slk[3] x[1] = 300 - x[3]*x[4]*cos(b - x[6])/a + c*x[3]^2*d/a x[2] = -x[3]*x[4]*cos(b + x[6])/a + c*x[4]^2*d/a x[5] = -x[3]*x[4]*sin(b + x[6])/a + c*x[4]^2*e/a 200 - x[3]*x[4]*sin(b - x[6])/a + c*x[3]^2*e/a = 0 ! best known objective = 8827.5977 obj[1] = rate[1]*x[1] + (rate[2]-rate[1])*add[1] obj[2] = rate[3]*x[2] + (rate[4]-rate[3])*add[2] + (rate[5]-rate[4])*add[3] End Equations End Model