* *************************** * SET UP THE INITIAL DATA * *************************** * Problem : * ********* * A quadratic obstacle problem by Dembo and Tulowitzki * The problem comes from the obstacle problem on a rectangle. * The rectangle is discretized into (px-1)(py-1) little rectangles. The * heights of the considered surface above the corners of these little * rectangles are the problem variables, There are px*py of them. * Source: * R. Dembo and U. Tulowitzki, * "On the minimization of quadratic functions subject to box * constraints", * WP 71, Yale University (new Haven, USA), 1983. * See also More 1989 (Problem B, Starting point U) * SIF input: Ph. Toint, Dec 1989. * classification QBR2-AY-V-0 * PX is the number of points along the X side of the rectangle * PY is the number of points along the Y side of the rectangle *IE PX 4 $ n = 16 *IE PY 4 *IE PX 23 $ n = 529 *IE PY 23 *IE PX 32 $ n = 1024 *IE PY 32 *IE PX 75 $ n = 5625 *IE PY 75 *IE PX 100 $ n = 10000 *IE PY 100 *IE PX 125 $ n = 15625 *IE PY 125 * The force constant * Define a few helpful parameters * Define one variable per discretized point in the unit square * Define a group per interior node * Fix the variables on the lower and upper edges of the unit square * Fix the variables on the left and right edges of the unit square * Describe the lower obstacle (problem B) * Describe the upper obstacle (problem B) * Start from the boundary values on the lower and upper edges * Start from the boundary values on the left and right edges * Describe the upper obstacle (starting point U) * Each node has four elements * Solution *LO SOLTN(4) -0.0081108 *LO SOLTN(10) 2.87503823 *LO SOLTN(23) 6.51932527 *LO SOLTN(32) 6.88708670 *LO SOLTN(75) ??? *LO SOLTN(100) ??? $offdigit; Parameter px ; px = 10; Parameter py ; py = 10; Parameter c ; c = 1.0; Parameter pxm1 ; pxm1 = -1 + (10); Parameter rpxm1 ; rpxm1 = 9.0; Parameter hx ; hx = 1.0 / (9.0); Parameter pym1 ; pym1 = -1 + (10); Parameter rpym1 ; rpym1 = 9.0; Parameter hy ; hy = 1.0 / (9.0); Parameter hxhy ; hxhy = (1.0 / (9.0)) * (1.0 / (9.0)); Parameter hxdhy ; hxdhy = (1.0 / (9.0)) * (1.0 / (1.0 / (9.0))); Parameter hydhx ; hydhx = (1.0 / (9.0)) * (1.0 / (1.0 / (9.0))); Parameter hyd4hx ; hyd4hx = 0.25 * ((1.0 / (9.0)) * (1.0 / (1.0 /(9.0)))); Parameter hxd4hy ; hxd4hy = 0.25 * ((1.0 / (9.0)) * (1.0 / (1.0 /(9.0)))); Parameter c0 ; c0 = ((1.0 / (9.0)) * (1.0 / (9.0))) * (1.0); Parameter lc ; lc = -1.0 * (((1.0 / (9.0)) * (1.0 / (9.0))) * (1.0)); Parameter im1 ; im1 = -1 + (9); Parameter rim1 ; rim1 = 8.0; Parameter xsi1 ; xsi1 = (8.0) * (1.0 / (9.0)); Parameter sxsi1 ; sxsi1 = sin(9.2 * ((8.0) * (1.0 / (9.0)))); Parameter jm1 ; jm1 = -1 + (9); Parameter rjm1 ; rjm1 = 8.0; Parameter xsi2 ; xsi2 = (8.0) * (1.0 / (9.0)); Parameter sxsi2 ; sxsi2 = sin(9.3 * ((8.0) * (1.0 / (9.0)))); Parameter l1 ; l1 = (sin(9.2 * ((8.0) * (1.0 / (9.0))))) * (sin(9.3 * ((8.0) * (1.0 /(9.0))))); Parameter l2 ; l2 = ((sin(9.2 * ((8.0) * (1.0 / (9.0))))) * (sin(9.3 * ((8.0) * (1.0 /(9.0)))))) * ((sin(9.2 * ((8.0) * (1/(9))))) * (sin(9.3 * ((8.0) * (1.0 /(9.0)))))); Parameter low ; low = (((sin(9.2 * ((8.0) * (1.0 / (9.0))))) * (sin(9.3 * ((8.0) * (1.0 /9))))) * ((sin(9.2 * ((8.0) * (1.0 / (9.0))))) * (sin(9.3 * ((8.0) * (1.0 /9)))))) * ((sin(9.2 * ((8.0) * (1.0 / (9.0))))) * (sin(9.3 * ((8.0) * (1.0 / (9.0)))))); Parameter upp ; upp = 0.02 + (((sin(9.2 * ((8.0) * (1.0 / (9.0))))) * (sin(9.3 * ((8.0) * (1/9))))) * ((sin(9.2 * ((8.0) * (1.0 / (9.0))))) * (sin(9.3 * ((8.0) * (1.0 / (9.0))))))); Parameter ip1 ; ip1 = 1 + (9); Parameter jp1 ; jp1 = 1 + (9); Positive Variable x1_1 , x2_1 , x3_1 , x4_1 , x5_1 , x6_1 , x7_1 , x8_1 , x9_1 , x10_1 , x1_2 , x2_2 , x3_2 , x4_2 , x8_2 , x9_2 , x10_2 , x1_3 , x2_3 , x3_3 , x4_3 , x8_3 , x9_3 , x10_3 , x1_4 , x2_4 , x3_4 , x4_4 , x8_4 , x9_4 , x10_4 , x1_5 , x5_5 , x6_5 , x7_5 , x10_5 , x1_6 , x5_6 , x6_6 , x7_6 , x10_6 , x1_7 , x5_7 , x6_7 , x7_7 , x10_7 , x1_8 , x2_8 , x3_8 , x4_8 , x8_8 , x9_8 , x10_8 , x1_9 , x2_9 , x3_9 , x4_9 , x8_9 , x9_9 , x10_9 , x1_10 ,x2_10 ,x3_10 ,x4_10 , x5_10 , x6_10 ,x7_10 ,x8_10 ,x9_10 ,x10_10 ; Variable x5_2 , x6_2 , x7_2 , x5_3 , x6_3 , x7_3 , x5_4 , x6_4 , x7_4 , x2_5 , x3_5 , x4_5 , x8_5 , x9_5 , x2_6 , x3_6 , x4_6 , x8_6 , x9_6 , x2_7 , x3_7 , x4_7 , x8_7 , x9_7 , x5_8 , x6_8 , x7_8 , x5_9 , x6_9 , x7_9 , obj ; Equation Def_obj ; Def_obj.. obj =e= 0.25*(x3_2-x2_2) * (x3_2-x2_2) + 0.25*(x2_3-x2_2) * (x2_3- x2_2) + 0.25*(x1_2-x2_2) * (x1_2-x2_2) + 0.25*(x2_1-x2_2) * (x2_1- x2_2) - 0.012345679012345678*x2_2 + 0.25*(x3_3-x2_3) * (x3_3-x2_3) + 0.25*(x2_4-x2_3) * (x2_4-x2_3) + 0.25*(x1_3-x2_3) * (x1_3-x2_3) + 0.25*(x2_2- x2_3) * (x2_2-x2_3) - 0.012345679012345678*x2_3 + 0.25*(x3_4-x2_4) * (x3_4-x2_4) + 0.25*(x2_5-x2_4) * (x2_5-x2_4) + 0.25*(x1_4-x2_4) * (x1_4-x2_4) + 0.25*(x2_3- x2_4) * (x2_3-x2_4) - 0.012345679012345678*x2_4 + 0.25*(x3_5-x2_5) * (x3_5-x2_5) + 0.25*(x2_6-x2_5) * (x2_6-x2_5) + 0.25*(x1_5-x2_5) * (x1_5-x2_5) + 0.25*(x2_4- x2_5) * (x2_4-x2_5) - 0.012345679012345678*x2_5 + 0.25*(x3_6-x2_6) * (x3_6-x2_6) + 0.25*(x2_7-x2_6) * (x2_7-x2_6) + 0.25*(x1_6-x2_6) * (x1_6-x2_6) + 0.25*(x2_5- x2_6) * (x2_5-x2_6) - 0.012345679012345678*x2_6 + 0.25*(x3_7-x2_7) * (x3_7-x2_7) + 0.25*(x2_8-x2_7) * (x2_8-x2_7) + 0.25*(x1_7-x2_7) * (x1_7-x2_7) + 0.25*(x2_6- x2_7) * (x2_6-x2_7) - 0.012345679012345678*x2_7 + 0.25*(x3_8-x2_8) * (x3_8-x2_8) + 0.25*(x2_9-x2_8) * (x2_9-x2_8) + 0.25*(x1_8-x2_8) * (x1_8-x2_8) + 0.25*(x2_7- x2_8) * (x2_7-x2_8) - 0.012345679012345678*x2_8 + 0.25*(x3_9-x2_9) * (x3_9-x2_9) + 0.25*(x2_10-x2_9) * (x2_10-x2_9) + 0.25*(x1_9-x2_9) * (x1_9-x2_9) + 0.25*(x2_8- x2_9) * (x2_8-x2_9) - 0.012345679012345678*x2_9 + 0.25*(x4_2-x3_2) * (x4_2-x3_2) + 0.25*(x3_3-x3_2) * (x3_3-x3_2) + 0.25*(x2_2-x3_2) * (x2_2- x3_2) + 0.25*(x3_1-x3_2) * (x3_1-x3_2) - 0.012345679012345678*x3_2 + 0.25*(x4_3-x3_3) * (x4_3-x3_3) + 0.25*(x3_4-x3_3) * (x3_4-x3_3) + 0.25*(x2_3- x3_3) * (x2_3-x3_3) + 0.25*(x3_2-x3_3) * (x3_2-x3_3) - 0.012345679012345678*x3_3 + 0.25*(x4_4-x3_4) * (x4_4-x3_4) + 0.25*(x3_5-x3_4) * (x3_5-x3_4) + 0.25*(x2_4- x3_4) * (x2_4-x3_4) + 0.25*(x3_3-x3_4) * (x3_3-x3_4) - 0.012345679012345678*x3_4 + 0.25*(x4_5-x3_5) * (x4_5-x3_5) + 0.25*(x3_6-x3_5) * (x3_6-x3_5) + 0.25*(x2_5- x3_5) * (x2_5-x3_5) + 0.25*(x3_4-x3_5) * (x3_4-x3_5) - 0.012345679012345678*x3_5 + 0.25*(x4_6-x3_6) * (x4_6-x3_6) + 0.25*(x3_7-x3_6) * (x3_7-x3_6) + 0.25*(x2_6- x3_6) * (x2_6-x3_6) + 0.25*(x3_5-x3_6) * (x3_5-x3_6) - 0.012345679012345678*x3_6 + 0.25*(x4_7-x3_7) * (x4_7-x3_7) + 0.25*(x3_8-x3_7) * (x3_8-x3_7) + 0.25*(x2_7- x3_7) * (x2_7-x3_7) + 0.25*(x3_6-x3_7) * (x3_6-x3_7) - 0.012345679012345678*x3_7 + 0.25*(x4_8-x3_8) * (x4_8-x3_8) + 0.25*(x3_9-x3_8) * (x3_9-x3_8) + 0.25*(x2_8- x3_8) * (x2_8-x3_8) + 0.25*(x3_7-x3_8) * (x3_7-x3_8) - 0.012345679012345678*x3_8 + 0.25*(x4_9-x3_9) * (x4_9-x3_9) + 0.25*(x3_10-x3_9) * (x3_10-x3_9) + 0.25*(x2_9- x3_9) * (x2_9-x3_9) + 0.25*(x3_8-x3_9) * (x3_8-x3_9) - 0.012345679012345678*x3_9 + 0.25*(x5_2-x4_2) * (x5_2-x4_2) + 0.25*(x4_3-x4_2) * (x4_3-x4_2) + 0.25*(x3_2- x4_2) * (x3_2-x4_2) + 0.25*(x4_1-x4_2) * (x4_1-x4_2) - 0.012345679012345678*x4_2 + 0.25*(x5_3-x4_3) * (x5_3-x4_3) + 0.25*(x4_4-x4_3) * (x4_4-x4_3) + 0.25*(x3_3- x4_3) * (x3_3-x4_3) + 0.25*(x4_2-x4_3) * (x4_2-x4_3) - 0.012345679012345678*x4_3 + 0.25*(x5_4-x4_4) * (x5_4-x4_4) + 0.25*(x4_5-x4_4) * (x4_5-x4_4) + 0.25*(x3_4- x4_4) * (x3_4-x4_4) + 0.25*(x4_3-x4_4) * (x4_3-x4_4) - 0.012345679012345678*x4_4 + 0.25*(x5_5-x4_5) * (x5_5-x4_5) + 0.25*(x4_6-x4_5) * (x4_6-x4_5) + 0.25*(x3_5- x4_5) * (x3_5-x4_5) + 0.25*(x4_4-x4_5) * (x4_4-x4_5) - 0.012345679012345678*x4_5 + 0.25*(x5_6-x4_6) * (x5_6-x4_6) + 0.25*(x4_7-x4_6) * (x4_7-x4_6) + 0.25*(x3_6- x4_6) * (x3_6-x4_6) + 0.25*(x4_5-x4_6) * (x4_5-x4_6) - 0.012345679012345678*x4_6 + 0.25*(x5_7-x4_7) * (x5_7-x4_7) + 0.25*(x4_8-x4_7) * (x4_8-x4_7) + 0.25*(x3_7- x4_7) * (x3_7-x4_7) + 0.25*(x4_6-x4_7) * (x4_6-x4_7) - 0.012345679012345678*x4_7 + 0.25*(x5_8-x4_8) * (x5_8-x4_8) + 0.25*(x4_9-x4_8) * (x4_9-x4_8) + 0.25*(x3_8- x4_8) * (x3_8-x4_8) + 0.25*(x4_7-x4_8) * (x4_7-x4_8) - 0.012345679012345678*x4_8 + 0.25*(x5_9-x4_9) * (x5_9-x4_9) + 0.25*(x4_10-x4_9) * (x4_10-x4_9) + 0.25*(x3_9- x4_9) * (x3_9-x4_9) + 0.25*(x4_8-x4_9) * (x4_8-x4_9) - 0.012345679012345678*x4_9 + 0.25*(x6_2-x5_2) * (x6_2-x5_2) + 0.25*(x5_3-x5_2) * (x5_3- x5_2) + 0.25*(x4_2-x5_2) * (x4_2-x5_2) + 0.25*(x5_1-x5_2) * (x5_1- x5_2) - 0.012345679012345678*x5_2 + 0.25*(x6_3-x5_3) * (x6_3-x5_3) + 0.25*(x5_4-x5_3) * (x5_4-x5_3) + 0.25*(x4_3-x5_3) * (x4_3-x5_3) + 0.25*(x5_2- x5_3) * (x5_2-x5_3) - 0.012345679012345678*x5_3 + 0.25*(x6_4-x5_4) * (x6_4-x5_4) + 0.25*(x5_5-x5_4) * (x5_5-x5_4) + 0.25*(x4_4-x5_4) * (x4_4-x5_4) + 0.25*(x5_3- x5_4) * (x5_3-x5_4) - 0.012345679012345678*x5_4 + 0.25*(x6_5-x5_5) * (x6_5-x5_5) + 0.25*(x5_6-x5_5) * (x5_6-x5_5) + 0.25*(x4_5-x5_5) * (x4_5-x5_5) + 0.25*(x5_4- x5_5) * (x5_4-x5_5) - 0.012345679012345678*x5_5 + 0.25*(x6_6-x5_6) * (x6_6-x5_6) + 0.25*(x5_7-x5_6) * (x5_7-x5_6) + 0.25*(x4_6-x5_6) * (x4_6-x5_6) + 0.25*(x5_5- x5_6) * (x5_5-x5_6) - 0.012345679012345678*x5_6 + 0.25*(x6_7-x5_7) * (x6_7-x5_7) + 0.25*(x5_8-x5_7) * (x5_8-x5_7) + 0.25*(x4_7-x5_7) * (x4_7-x5_7) + 0.25*(x5_6- x5_7) * (x5_6-x5_7) - 0.012345679012345678*x5_7 + 0.25*(x6_8-x5_8) * (x6_8-x5_8) + 0.25*(x5_9-x5_8) * (x5_9-x5_8) + 0.25*(x4_8-x5_8) * (x4_8-x5_8) + 0.25*(x5_7- x5_8) * (x5_7-x5_8) - 0.012345679012345678*x5_8 + 0.25*(x6_9-x5_9) * (x6_9-x5_9) + 0.25*(x5_10-x5_9) * (x5_10-x5_9) + 0.25*(x4_9-x5_9) * (x4_9-x5_9) + 0.25*(x5_8- x5_9) * (x5_8-x5_9) - 0.012345679012345678*x5_9 + 0.25*(x7_2-x6_2) * (x7_2-x6_2) + 0.25*(x6_3-x6_2) * (x6_3-x6_2) + 0.25*(x5_2-x6_2) * (x5_2- x6_2) + 0.25*(x6_1-x6_2) * (x6_1-x6_2) - 0.012345679012345678*x6_2 + 0.25*(x7_3-x6_3) * (x7_3-x6_3) + 0.25*(x6_4-x6_3) * (x6_4-x6_3) + 0.25*(x5_3- x6_3) * (x5_3-x6_3) + 0.25*(x6_2-x6_3) * (x6_2-x6_3) - 0.012345679012345678*x6_3 + 0.25*(x7_4-x6_4) * (x7_4-x6_4) + 0.25*(x6_5-x6_4) * (x6_5-x6_4) + 0.25*(x5_4- x6_4) * (x5_4-x6_4) + 0.25*(x6_3-x6_4) * (x6_3-x6_4) - 0.012345679012345678*x6_4 + 0.25*(x7_5-x6_5) * (x7_5-x6_5) + 0.25*(x6_6-x6_5) * (x6_6-x6_5) + 0.25*(x5_5- x6_5) * (x5_5-x6_5) + 0.25*(x6_4-x6_5) * (x6_4-x6_5) - 0.012345679012345678*x6_5 + 0.25*(x7_6-x6_6) * (x7_6-x6_6) + 0.25*(x6_7-x6_6) * (x6_7-x6_6) + 0.25*(x5_6- x6_6) * (x5_6-x6_6) + 0.25*(x6_5-x6_6) * (x6_5-x6_6) - 0.012345679012345678*x6_6 + 0.25*(x7_7-x6_7) * (x7_7-x6_7) + 0.25*(x6_8-x6_7) * (x6_8-x6_7) + 0.25*(x5_7- x6_7) * (x5_7-x6_7) + 0.25*(x6_6-x6_7) * (x6_6-x6_7) - 0.012345679012345678*x6_7 + 0.25*(x7_8-x6_8) * (x7_8-x6_8) + 0.25*(x6_9-x6_8) * (x6_9-x6_8) + 0.25*(x5_8- x6_8) * (x5_8-x6_8) + 0.25*(x6_7-x6_8) * (x6_7-x6_8) - 0.012345679012345678*x6_8 + 0.25*(x7_9-x6_9) * (x7_9-x6_9) + 0.25*(x6_10-x6_9) * (x6_10-x6_9) + 0.25*(x5_9- x6_9) * (x5_9-x6_9) + 0.25*(x6_8-x6_9) * (x6_8-x6_9) - 0.012345679012345678*x6_9 + 0.25*(x8_2-x7_2) * (x8_2-x7_2) + 0.25*(x7_3-x7_2) * (x7_3-x7_2) + 0.25*(x6_2- x7_2) * (x6_2-x7_2) + 0.25*(x7_1-x7_2) * (x7_1-x7_2) - 0.012345679012345678*x7_2 + 0.25*(x8_3-x7_3) * (x8_3-x7_3) + 0.25*(x7_4-x7_3) * (x7_4-x7_3) + 0.25*(x6_3- x7_3) * (x6_3-x7_3) + 0.25*(x7_2-x7_3) * (x7_2-x7_3) - 0.012345679012345678*x7_3 + 0.25*(x8_4-x7_4) * (x8_4-x7_4) + 0.25*(x7_5-x7_4) * (x7_5-x7_4) + 0.25*(x6_4- x7_4) * (x6_4-x7_4) + 0.25*(x7_3-x7_4) * (x7_3-x7_4) - 0.012345679012345678*x7_4 + 0.25*(x8_5-x7_5) * (x8_5-x7_5) + 0.25*(x7_6-x7_5) * (x7_6-x7_5) + 0.25*(x6_5- x7_5) * (x6_5-x7_5) + 0.25*(x7_4-x7_5) * (x7_4-x7_5) - 0.012345679012345678*x7_5 + 0.25*(x8_6-x7_6) * (x8_6-x7_6) + 0.25*(x7_7-x7_6) * (x7_7-x7_6) + 0.25*(x6_6- x7_6) * (x6_6-x7_6) + 0.25*(x7_5-x7_6) * (x7_5-x7_6) - 0.012345679012345678*x7_6 + 0.25*(x8_7-x7_7) * (x8_7-x7_7) + 0.25*(x7_8-x7_7) * (x7_8-x7_7) + 0.25*(x6_7- x7_7) * (x6_7-x7_7) + 0.25*(x7_6-x7_7) * (x7_6-x7_7) - 0.012345679012345678*x7_7 + 0.25*(x8_8-x7_8) * (x8_8-x7_8) + 0.25*(x7_9-x7_8) * (x7_9-x7_8) + 0.25*(x6_8- x7_8) * (x6_8-x7_8) + 0.25*(x7_7-x7_8) * (x7_7-x7_8) - 0.012345679012345678*x7_8 + 0.25*(x8_9-x7_9) * (x8_9-x7_9) + 0.25*(x7_10-x7_9) * (x7_10-x7_9) + 0.25*(x6_9- x7_9) * (x6_9-x7_9) + 0.25*(x7_8-x7_9) * (x7_8-x7_9) - 0.012345679012345678*x7_9 + 0.25*(x9_2-x8_2) * (x9_2-x8_2) + 0.25*(x8_3-x8_2) * (x8_3- x8_2) + 0.25*(x7_2-x8_2) * (x7_2-x8_2) + 0.25*(x8_1-x8_2) * (x8_1- x8_2) - 0.012345679012345678*x8_2 + 0.25*(x9_3-x8_3) * (x9_3-x8_3) + 0.25*(x8_4-x8_3) * (x8_4-x8_3) + 0.25*(x7_3-x8_3) * (x7_3-x8_3) + 0.25*(x8_2- x8_3) * (x8_2-x8_3) - 0.012345679012345678*x8_3 + 0.25*(x9_4-x8_4) * (x9_4-x8_4) + 0.25*(x8_5-x8_4) * (x8_5-x8_4) + 0.25*(x7_4-x8_4) * (x7_4-x8_4) + 0.25*(x8_3- x8_4) * (x8_3-x8_4) - 0.012345679012345678*x8_4 + 0.25*(x9_5-x8_5) * (x9_5-x8_5) + 0.25*(x8_6-x8_5) * (x8_6-x8_5) + 0.25*(x7_5-x8_5) * (x7_5-x8_5) + 0.25*(x8_4- x8_5) * (x8_4-x8_5) - 0.012345679012345678*x8_5 + 0.25*(x9_6-x8_6) * (x9_6-x8_6) + 0.25*(x8_7-x8_6) * (x8_7-x8_6) + 0.25*(x7_6-x8_6) * (x7_6-x8_6) + 0.25*(x8_5- x8_6) * (x8_5-x8_6) - 0.012345679012345678*x8_6 + 0.25*(x9_7-x8_7) * (x9_7-x8_7) + 0.25*(x8_8-x8_7) * (x8_8-x8_7) + 0.25*(x7_7-x8_7) * (x7_7-x8_7) + 0.25*(x8_6- x8_7) * (x8_6-x8_7) - 0.012345679012345678*x8_7 + 0.25*(x9_8-x8_8) * (x9_8-x8_8) + 0.25*(x8_9-x8_8) * (x8_9-x8_8) + 0.25*(x7_8-x8_8) * (x7_8-x8_8) + 0.25*(x8_7- x8_8) * (x8_7-x8_8) - 0.012345679012345678*x8_8 + 0.25*(x9_9-x8_9) * (x9_9-x8_9) + 0.25*(x8_10-x8_9) * (x8_10-x8_9) + 0.25*(x7_9-x8_9) * (x7_9-x8_9) + 0.25*(x8_8- x8_9) * (x8_8-x8_9) - 0.012345679012345678*x8_9 + 0.25*(x10_2-x9_2) * (x10_2-x9_2) + 0.25*(x9_3-x9_2) * (x9_3-x9_2) + 0.25*(x8_2-x9_2) * (x8_2- x9_2) + 0.25*(x9_1-x9_2) *(x9_1-x9_2) - 0.012345679012345678*x9_2 + 0.25*(x10_3-x9_3) * (x10_3-x9_3) + 0.25*(x9_4-x9_3) * (x9_4-x9_3) + 0.25*(x8_3- x9_3) * (x8_3-x9_3) + 0.25*(x9_2-x9_3) * (x9_2-x9_3) - 0.012345679012345678*x9_3 + 0.25*(x10_4-x9_4) * (x10_4-x9_4) + 0.25*(x9_5-x9_4) * (x9_5- x9_4) + 0.25*(x8_4-x9_4) * (x8_4-x9_4) + 0.25*(x9_3-x9_4) * (x9_3- x9_4) - 0.012345679012345678*x9_4 + 0.25*(x10_5-x9_5) * (x10_5-x9_5) + 0.25*(x9_6-x9_5) * (x9_6-x9_5) + 0.25*(x8_5-x9_5) * (x8_5-x9_5) + 0.25*(x9_4- x9_5) * (x9_4-x9_5) - 0.012345679012345678*x9_5 + 0.25*(x10_6-x9_6) * (x10_6- x9_6) + 0.25*(x9_7-x9_6) * (x9_7-x9_6) + 0.25*(x8_6-x9_6) * (x8_6- x9_6) + 0.25*(x9_5-x9_6) * (x9_5-x9_6) - 0.012345679012345678*x9_6 + 0.25*(x10_7-x9_7) * (x10_7-x9_7) + 0.25*(x9_8-x9_7) * (x9_8-x9_7) + 0.25*(x8_7- x9_7) * (x8_7-x9_7) + 0.25*(x9_6-x9_7) * (x9_6-x9_7) - 0.012345679012345678*x9_7 + 0.25*(x10_8-x9_8) * (x10_8-x9_8) + 0.25*(x9_9-x9_8) * (x9_9- x9_8) + 0.25*(x8_8-x9_8) * (x8_8-x9_8) + 0.25*(x9_7-x9_8) * (x9_7- x9_8) - 0.012345679012345678*x9_8 + 0.25*(x10_9-x9_9) * (x10_9-x9_9) + 0.25*(x9_10-x9_9) * (x9_10-x9_9) + 0.25*(x8_9-x9_9) * (x8_9- x9_9) + 0.25*(x9_8-x9_9) * (x9_8-x9_9) - 0.012345679012345678*x9_9; x1_1.up =0.0 ; x2_1.up =0.0 ; x3_1.up =0.0 ; x4_1.up =0.0 ; x5_1.up =0.0 ; x6_1.up =0.0 ; x7_1.up =0.0 ; x8_1.up =0.0 ; x9_1.up =0.0 ; x10_1.up =0.0 ; x1_2.up =0.0 ; x10_2.up =0.0 ; x1_3.up =0.0 ; x10_3.up =0.0 ; x1_4.up =0.0 ; x10_4.up =0.0 ; x1_5.up =0.0 ; x10_5.up =0.0 ; x1_6.up =0.0 ; x10_6.up =0.0 ; x1_7.up =0.0 ; x10_7.up =0.0 ; x1_8.up =0.0 ; x10_8.up =0.0 ; x1_9.up =0.0 ; x10_9.up =0.0 ; x1_10.up =0.0 ; x2_10.up =0.0 ; x3_10.up =0.0 ; x4_10.up =0.0 ; x5_10.up =0.0 ; x6_10.up =0.0 ; x7_10.up =0.0 ; x8_10.up =0.0 ; x9_10.up =0.0 ; x10_10.up =0.0 ; x2_2.lo = 0.3937793366356831 ; x2_2.up = 0.5572403400857789 ; x3_2.lo = 0.44671816460760055 ; x3_2.up = 0.6043715642572578 ; x4_2.lo = 2.658723886528665e-4 ; x4_2.up = 0.02413474589705515 ; x5_2.lo = -0.3391611563540678 ; x5_2.up = 0.5063371045723885 ; x6_2.lo = -0.4960928025216343 ; x6_2.up = 0.6466743955359259 ; x7_2.lo = -0.0021091266848867365; x7_2.up = 0.036446308947150105; x8_2.lo = 0.2847312063379939 ; x8_2.up = 0.4528027837130198 ; x9_2.lo = 0.5400916195594984 ; x9_2.up = 0.6832006741551072 ; x2_3.lo = 0.4227141086543548 ; x2_3.up = 0.5832456273206106 ; x3_3.lo = 0.4795428637397414 ; x3_3.up = 0.632658253186744 ; x4_3.lo = 2.854086015416797e-4 ; x4_3.up = 0.024334889569585016; x5_3.lo = -0.36408260302147705 ; x5_3.up = 0.5298784047199946 ; x6_3.lo = -0.5325455332913744 ; x6_3.up = 0.6770087662870579 ; x7_3.lo = -0.0022641045979156157; x7_3.up = 0.0372423976921895 ; x8_3.lo = 0.30565315875017296 ; x8_3.up = 0.47375273826165754 ; x9_3.lo = 0.5797773684732547 ; x9_3.up = 0.7153031108838603 ; x2_4.lo = 4.466137010418048e-5 ; x2_4.up = 0.021258794088429997; x3_4.lo = 5.0665546476499324e-5; x3_4.up = 0.021369226053308238; x4_4.lo = 3.0154515601447075e-8; x4_4.up = 0.020009688017269035; x5_4.lo = -3.846672620840164e-5 ; x5_4.up = 0.021139524020333502; x6_4.lo = -5.626548220821779e-5 ; x6_4.up = 0.021468344734397852; x7_4.lo = -2.3921135190869225e-7; x7_4.up = 0.020038534925496957; x8_4.lo = 3.229343087201135e-5 ; x8_4.up = 0.021014089123514084; x9_4.lo = 6.125570711098406e-5 ; x9_4.up = 0.021553928522820797; x2_5.lo = -0.3642526902031173 ; x2_5.up = 0.5300371910853469 ; x3_5.lo = -0.41322202076708053 ; x3_5.up = 0.5747819270912036 ; x4_5.lo = -2.4593655331166914e-4; x4_5.up = 0.023925383158772025; x5_5.lo = 0.3137299297364258 ; x5_5.up = 0.4817114394222081 ; x6_5.lo = 0.4588944139445591 ; x6_5.up = 0.6149427557379955 ; x7_5.lo = 0.0019509786255238442; x7_5.up = 0.035613550571773775; x8_5.lo = -0.2633812855176486 ; x8_5.up = 0.4308878273430881 ; x9_5.lo = -0.49959407992684074 ; x9_5.up = 0.6496195273012655 ; x2_6.lo = -0.4507393756992777 ; x2_6.up = 0.6078732052695588 ; x3_6.lo = -0.5113357860497522 ; x3_6.up = 0.6594463686279571 ; x4_6.lo = -3.043307338087716e-4 ; x4_6.up = 0.024524430021559566; x5_6.lo = 0.3882206953330132 ; x5_6.up = 0.5521725328013108 ; x6_6.lo = 0.5678524475355717 ; x6_6.up = 0.705736081369553 ; x7_6.lo = 0.002414211099390602 ; x7_6.up = 0.03799631121160941 ; x8_6.lo = -0.3259174726723327 ; x8_6.up = 0.49359280516860704 ; x9_6.lo = -0.618215677593785 ; x9_6.up = 0.7457048232644721 ; x2_7.lo = -3.5636475335626487e-4; x2_7.up = 0.02502647077806891 ; x3_7.lo = -4.0427364703860696e-4; x3_7.up = 0.025467434911541704; x4_7.lo = -2.4061076697424153e-7; x4_7.up = 0.02003868506862863 ; x5_7.lo = 3.0693606948696984e-4; x5_7.up = 0.024550215354329948; x6_7.lo = 4.489569989194305e-4 ; x6_7.up = 0.025863224150335377; x7_7.lo = 1.9087299432173126e-6; x7_7.up = 0.02015387320192066 ; x8_7.lo = -2.576777313568063e-4 ; x8_7.up = 0.02404934325045849 ; x9_7.lo = -4.887753086246255e-4 ; x9_7.up = 0.026204967423153654; x2_8.lo = 0.3344514359720908 ; x2_8.up = 0.5018243120191268 ; x3_8.lo = 0.37941435145962443 ; x3_8.up = 0.544093977877458 ; x4_8.lo = 2.2581530795900886e-4; x4_8.up = 0.023708249266807507; x5_8.lo = -0.28806218410977386 ; x5_8.up = 0.4561717155911093 ; x6_8.lo = -0.4213500677723075 ; x6_8.up = 0.5820332967566972 ; x7_8.lo = -0.001791359735719315 ; x7_8.up = 0.03474988176139078 ; x8_8.lo = 0.24183280321260603 ; x8_8.up = 0.4081594287375977 ; x9_8.lo = 0.45871989947833597 ; x9_8.up = 0.6147919110176742 ; x2_9.lo = 0.4775418533990749 ; x2_9.up = 0.6309527543824225 ; x3_9.lo = 0.5417415299043793 ; x3_9.up = 0.684550649172644 ; x4_9.lo = 3.224272617493759e-4 ; x4_9.up = 0.024702056427992596; x5_9.lo = -0.41130560224428553 ; x5_9.up = 0.573065306952623 ; x6_9.lo = -0.6016188619701556 ; x6_9.up = 0.732657668246734 ; x7_9.lo = -0.0025577682027690973; x7_9.up = 0.038702835585803785; x8_9.lo = 0.3452976206341617 ; x8_9.up = 0.5121857743810341 ; x9_9.lo = 0.6549768589009787 ; x9_9.up = 0.7741955589534621 ; x2_2.l = 0.5572403400857789 ; x3_2.l = 0.6043715642572578 ; x4_2.l = 0.02413474589705515 ; x5_2.l = 0.5063371045723885 ; x6_2.l = 0.6466743955359259 ; x7_2.l = 0.036446308947150105; x8_2.l = 0.4528027837130198 ; x9_2.l = 0.6832006741551072 ; x2_3.l = 0.5832456273206106 ; x3_3.l = 0.632658253186744 ; x4_3.l = 0.024334889569585016; x5_3.l = 0.5298784047199946 ; x6_3.l = 0.6770087662870579 ; x7_3.l = 0.0372423976921895 ; x8_3.l = 0.47375273826165754 ; x9_3.l = 0.7153031108838603 ; x2_4.l = 0.021258794088429997; x3_4.l = 0.021369226053308238; x4_4.l = 0.020009688017269035; x5_4.l = 0.021139524020333502; x6_4.l = 0.021468344734397852; x7_4.l = 0.020038534925496957; x8_4.l = 0.021014089123514084; x9_4.l = 0.021553928522820797; x2_5.l = 0.5300371910853469 ; x3_5.l = 0.5747819270912036 ; x4_5.l = 0.023925383158772025; x5_5.l = 0.4817114394222081 ; x6_5.l = 0.6149427557379955 ; x7_5.l = 0.035613550571773775; x8_5.l = 0.4308878273430881 ; x9_5.l = 0.6496195273012655 ; x2_6.l = 0.6078732052695588 ; x3_6.l = 0.6594463686279571 ; x4_6.l = 0.024524430021559566; x5_6.l = 0.5521725328013108 ; x6_6.l = 0.705736081369553 ; x7_6.l = 0.03799631121160941 ; x8_6.l = 0.49359280516860704 ; x9_6.l = 0.7457048232644721 ; x2_7.l = 0.02502647077806891 ; x3_7.l = 0.025467434911541704; x4_7.l = 0.02003868506862863 ; x5_7.l = 0.024550215354329948; x6_7.l = 0.025863224150335377; x7_7.l = 0.02015387320192066 ; x8_7.l = 0.02404934325045849 ; x9_7.l = 0.026204967423153654; x2_8.l = 0.5018243120191268 ; x3_8.l = 0.544093977877458 ; x4_8.l = 0.023708249266807507; x5_8.l = 0.4561717155911093 ; x6_8.l = 0.5820332967566972 ; x7_8.l = 0.03474988176139078 ; x8_8.l = 0.4081594287375977 ; x9_8.l = 0.6147919110176742 ; x2_9.l = 0.6309527543824225 ; x3_9.l = 0.684550649172644 ; x4_9.l = 0.024702056427992596; x5_9.l = 0.573065306952623 ; x6_9.l = 0.732657668246734 ; x7_9.l = 0.038702835585803785; x8_9.l = 0.5121857743810341 ; x9_9.l = 0.7741955589534621 ; Model obstclbu /all/ ; Solve obstclbu using nlp minimazing obj ; display x1_1.l ; display x2_1.l ; display x3_1.l ; display x4_1.l ; display x5_1.l ; display x6_1.l ; display x7_1.l ; display x8_1.l ; display x9_1.l ; display x10_1.l ; display x1_2.l ; display x2_2.l ; display x3_2.l ; display x4_2.l ; display x5_2.l ; display x6_2.l ; display x7_2.l ; display x8_2.l ; display x9_2.l ; display x10_2.l ; display x1_3.l ; display x2_3.l ; display x3_3.l ; display x4_3.l ; display x5_3.l ; display x6_3.l ; display x7_3.l ; display x8_3.l ; display x9_3.l ; display x10_3.l ; display x1_4.l ; display x2_4.l ; display x3_4.l ; display x4_4.l ; display x5_4.l ; display x6_4.l ; display x7_4.l ; display x8_4.l ; display x9_4.l ; display x10_4.l ; display x1_5.l ; display x2_5.l ; display x3_5.l ; display x4_5.l ; display x5_5.l ; display x6_5.l ; display x7_5.l ; display x8_5.l ; display x9_5.l ; display x10_5.l ; display x1_6.l ; display x2_6.l ; display x3_6.l ; display x4_6.l ; display x5_6.l ; display x6_6.l ; display x7_6.l ; display x8_6.l ; display x9_6.l ; display x10_6.l ; display x1_7.l ; display x2_7.l ; display x3_7.l ; display x4_7.l ; display x5_7.l ; display x6_7.l ; display x7_7.l ; display x8_7.l ; display x9_7.l ; display x10_7.l ; display x1_8.l ; display x2_8.l ; display x3_8.l ; display x4_8.l ; display x5_8.l ; display x6_8.l ; display x7_8.l ; display x8_8.l ; display x9_8.l ; display x10_8.l ; display x1_9.l ; display x2_9.l ; display x3_9.l ; display x4_9.l ; display x5_9.l ; display x6_9.l ; display x7_9.l ; display x8_9.l ; display x9_9.l ; display x10_9.l ; display x1_10.l ; display x2_10.l ; display x3_10.l ; display x4_10.l ; display x5_10.l ; display x6_10.l ; display x7_10.l ; display x8_10.l ; display x9_10.l ; display x10_10.l ; display obj.l ;