#
#**************************
# SET UP THE INITIAL DATA *
#**************************
#   Problem :
#   *********
#   A problem freely inspired by the heavy spacecraft landing problem by
#   Ivashkevich, as reported by Tyatushkin, Zholudev and Erinchek.  The
#   modifications of the original problem involves dropping the final state
#   constraint on the second variable and the setting of EPS to zero
#   in the second constraint. 
#   (No feasible point was found for the original formulation by any of the
#   packages at hand.)
#   This is a badly scaled degenerate nonlinear nonconvex optimal control 
#   problem, with lots of negative curvature.
#   Source: inspired by
#   A.I Tyatushkin, A.I. Zholudev and N. M. Erinchek,
#   "The gradient method for solving optimal control problems with phase
#   constraints", 
#   in "System Modelling and Optimization", P. Kall, ed., pp. 456--464,
#   Springer Verlag, Lecture Notes in Control and Information Sciences 180, 1992.
#   This reference itself refers to:
#   A.K. Ivashkevich,
#   "Multistage US spacecraft Space Shuttle", 
#   Survey of foreign papers (Part 11),  Orbital Craft, Moscow, 1976.
#   SIF input: Ph. Toint, February 1994.
#   classification LOR2-AN-V-V
#   Number of discretized points in (0,TT].
#   The number of variables is    4 * ( N + 1 )
#   The number of constraints is  3 * N
#IE N                   100            $ n =  404, m =  300
#IE N                   500            $ n = 2004, m = 1500
#IE N                   1000           $ n = 4004, m = 3000
#   Problem parameters
#   Mesh
#   Constants
#   State variables
#   Control variables
#   Objective function
#   State constraints
#   State constraints elements
#   State constraints
# ZE C(2,T)    E2(T)                    -H
# ZE C(2,T)    E3(T)                    -H
#   Solution
#LO SOLTN             -0.21850
#LO SOLTN(100)        3.26705331D-8
#LO SOLTN(500)        2.36171208D-8
#LO SOLTN(1000)       8.48265630D-8
param n := 50;
param tt := 0.2185;
param eps := 0.1;
param alpha := 1.62079;
param nm1 := -1 + (50);
param rn := 50.0;
param h := (0.2185) / (50.0);
param tm1 := -1 + (50);

var x1_0 >= 0.0 ,  <= 0.0;
var x2_0 >= 2.19905 ,  <= 2.19905 ,  := 2.19905;
var x3_0 >= 0.0 ,  <= 6.2831854;
var x1_1;
var x2_1 := 1.5;
var x3_1 >= 0.0 ,  <= 6.2831854;
var x1_2;
var x2_2 := 1.5;
var x3_2 >= 0.0 ,  <= 6.2831854;
var x1_3;
var x2_3 := 1.5;
var x3_3 >= 0.0 ,  <= 6.2831854;
var x1_4;
var x2_4 := 1.5;
var x3_4 >= 0.0 ,  <= 6.2831854;
var x1_5;
var x2_5 := 1.5;
var x3_5 >= 0.0 ,  <= 6.2831854;
var x1_6;
var x2_6 := 1.5;
var x3_6 >= 0.0 ,  <= 6.2831854;
var x1_7;
var x2_7 := 1.5;
var x3_7 >= 0.0 ,  <= 6.2831854;
var x1_8;
var x2_8 := 1.5;
var x3_8 >= 0.0 ,  <= 6.2831854;
var x1_9;
var x2_9 := 1.5;
var x3_9 >= 0.0 ,  <= 6.2831854;
var x1_10;
var x2_10 := 1.5;
var x3_10 >= 0.0 ,  <= 6.2831854;
var x1_11;
var x2_11 := 1.5;
var x3_11 >= 0.0 ,  <= 6.2831854;
var x1_12;
var x2_12 := 1.5;
var x3_12 >= 0.0 ,  <= 6.2831854;
var x1_13;
var x2_13 := 1.5;
var x3_13 >= 0.0 ,  <= 6.2831854;
var x1_14;
var x2_14 := 1.5;
var x3_14 >= 0.0 ,  <= 6.2831854;
var x1_15;
var x2_15 := 1.5;
var x3_15 >= 0.0 ,  <= 6.2831854;
var x1_16;
var x2_16 := 1.5;
var x3_16 >= 0.0 ,  <= 6.2831854;
var x1_17;
var x2_17 := 1.5;
var x3_17 >= 0.0 ,  <= 6.2831854;
var x1_18;
var x2_18 := 1.5;
var x3_18 >= 0.0 ,  <= 6.2831854;
var x1_19;
var x2_19 := 1.5;
var x3_19 >= 0.0 ,  <= 6.2831854;
var x1_20;
var x2_20 := 1.5;
var x3_20 >= 0.0 ,  <= 6.2831854;
var x1_21;
var x2_21 := 1.5;
var x3_21 >= 0.0 ,  <= 6.2831854;
var x1_22;
var x2_22 := 1.5;
var x3_22 >= 0.0 ,  <= 6.2831854;
var x1_23;
var x2_23 := 1.5;
var x3_23 >= 0.0 ,  <= 6.2831854;
var x1_24;
var x2_24 := 1.5;
var x3_24 >= 0.0 ,  <= 6.2831854;
var x1_25;
var x2_25 := 1.5;
var x3_25 >= 0.0 ,  <= 6.2831854;
var x1_26;
var x2_26 := 1.5;
var x3_26 >= 0.0 ,  <= 6.2831854;
var x1_27;
var x2_27 := 1.5;
var x3_27 >= 0.0 ,  <= 6.2831854;
var x1_28;
var x2_28 := 1.5;
var x3_28 >= 0.0 ,  <= 6.2831854;
var x1_29;
var x2_29 := 1.5;
var x3_29 >= 0.0 ,  <= 6.2831854;
var x1_30;
var x2_30 := 1.5;
var x3_30 >= 0.0 ,  <= 6.2831854;
var x1_31;
var x2_31 := 1.5;
var x3_31 >= 0.0 ,  <= 6.2831854;
var x1_32;
var x2_32 := 1.5;
var x3_32 >= 0.0 ,  <= 6.2831854;
var x1_33;
var x2_33 := 1.5;
var x3_33 >= 0.0 ,  <= 6.2831854;
var x1_34;
var x2_34 := 1.5;
var x3_34 >= 0.0 ,  <= 6.2831854;
var x1_35;
var x2_35 := 1.5;
var x3_35 >= 0.0 ,  <= 6.2831854;
var x1_36;
var x2_36 := 1.5;
var x3_36 >= 0.0 ,  <= 6.2831854;
var x1_37;
var x2_37 := 1.5;
var x3_37 >= 0.0 ,  <= 6.2831854;
var x1_38;
var x2_38 := 1.5;
var x3_38 >= 0.0 ,  <= 6.2831854;
var x1_39;
var x2_39 := 1.5;
var x3_39 >= 0.0 ,  <= 6.2831854;
var x1_40;
var x2_40 := 1.5;
var x3_40 >= 0.0 ,  <= 6.2831854;
var x1_41;
var x2_41 := 1.5;
var x3_41 >= 0.0 ,  <= 6.2831854;
var x1_42;
var x2_42 := 1.5;
var x3_42 >= 0.0 ,  <= 6.2831854;
var x1_43;
var x2_43 := 1.5;
var x3_43 >= 0.0 ,  <= 6.2831854;
var x1_44;
var x2_44 := 1.5;
var x3_44 >= 0.0 ,  <= 6.2831854;
var x1_45;
var x2_45 := 1.5;
var x3_45 >= 0.0 ,  <= 6.2831854;
var x1_46;
var x2_46 := 1.5;
var x3_46 >= 0.0 ,  <= 6.2831854;
var x1_47;
var x2_47 := 1.5;
var x3_47 >= 0.0 ,  <= 6.2831854;
var x1_48;
var x2_48 := 1.5;
var x3_48 >= 0.0 ,  <= 6.2831854;
var x1_49;
var x2_49 := 1.5;
var x3_49 >= 0.0 ,  <= 6.2831854;
var x1_50;
var x2_50 := 1.09905;
var x3_50 >= 0.0 ,  <= 6.2831854;
var u0 >= 0.08 ,  <= 0.417;
var u1 >= 0.08 ,  <= 0.417;
var u2 >= 0.08 ,  <= 0.417;
var u3 >= 0.08 ,  <= 0.417;
var u4 >= 0.08 ,  <= 0.417;
var u5 >= 0.08 ,  <= 0.417;
var u6 >= 0.08 ,  <= 0.417;
var u7 >= 0.08 ,  <= 0.417;
var u8 >= 0.08 ,  <= 0.417;
var u9 >= 0.08 ,  <= 0.417;
var u10 >= 0.08 ,  <= 0.417;
var u11 >= 0.08 ,  <= 0.417;
var u12 >= 0.08 ,  <= 0.417;
var u13 >= 0.08 ,  <= 0.417;
var u14 >= 0.08 ,  <= 0.417;
var u15 >= 0.08 ,  <= 0.417;
var u16 >= 0.08 ,  <= 0.417;
var u17 >= 0.08 ,  <= 0.417;
var u18 >= 0.08 ,  <= 0.417;
var u19 >= 0.08 ,  <= 0.417;
var u20 >= 0.08 ,  <= 0.417;
var u21 >= 0.08 ,  <= 0.417;
var u22 >= 0.08 ,  <= 0.417;
var u23 >= 0.08 ,  <= 0.417;
var u24 >= 0.08 ,  <= 0.417;
var u25 >= 0.08 ,  <= 0.417;
var u26 >= 0.08 ,  <= 0.417;
var u27 >= 0.08 ,  <= 0.417;
var u28 >= 0.08 ,  <= 0.417;
var u29 >= 0.08 ,  <= 0.417;
var u30 >= 0.08 ,  <= 0.417;
var u31 >= 0.08 ,  <= 0.417;
var u32 >= 0.08 ,  <= 0.417;
var u33 >= 0.08 ,  <= 0.417;
var u34 >= 0.08 ,  <= 0.417;
var u35 >= 0.08 ,  <= 0.417;
var u36 >= 0.08 ,  <= 0.417;
var u37 >= 0.08 ,  <= 0.417;
var u38 >= 0.08 ,  <= 0.417;
var u39 >= 0.08 ,  <= 0.417;
var u40 >= 0.08 ,  <= 0.417;
var u41 >= 0.08 ,  <= 0.417;
var u42 >= 0.08 ,  <= 0.417;
var u43 >= 0.08 ,  <= 0.417;
var u44 >= 0.08 ,  <= 0.417;
var u45 >= 0.08 ,  <= 0.417;
var u46 >= 0.08 ,  <= 0.417;
var u47 >= 0.08 ,  <= 0.417;
var u48 >= 0.08 ,  <= 0.417;
var u49 >= 0.08 ,  <= 0.417;
var u50 >= 0.08 ,  <= 0.417;

minimize obj:
	x1_50;

subject to c1_1:
	0.00437*(cos(x3_1)) / (1.62079*(0.01+0.3*u1*u1)*x2_1*x2_1) + x1_0 - x1_1 = 0;
subject to c2_1:
	-1.0 / x2_1 - (cos(x3_1)) / (1.62079*(0.01+0.3*u1*u1)*(x2_1*x2_1)*x2_1) = 0;
subject to c3_1:
	0.00437*u1 / ((0.01+0.3*u1*u1) * (x2_1*x2_1) )  - 0.00437*(cos(x3_1)) / (1.62079*(0.01+0.3*u1*u1)*(x2_1*x2_1)*x2_1*x2_1) + 0.1*x3_0 - 0.1*x3_1 = 0;
subject to c1_2:
	0.00437*(cos(x3_2)) / (1.62079*(0.01+0.3*u2*u2)*x2_2*x2_2) + x1_1 - x1_2 = 0;
subject to c2_2:
	-1.0 / x2_2 - (cos(x3_2)) / (1.62079*(0.01+0.3*u2*u2)*(x2_2*x2_2)*x2_2) = 0;
subject to c3_2:
	0.00437*u2 / ((0.01+0.3*u2*u2) * (x2_2*x2_2) )  - 0.00437*(cos(x3_2)) / (1.62079*(0.01+0.3*u2*u2)*(x2_2*x2_2)*x2_2*x2_2) + 0.1*x3_1 - 0.1*x3_2 = 0;
subject to c1_3:
	0.00437*(cos(x3_3)) / (1.62079*(0.01+0.3*u3*u3)*x2_3*x2_3) + x1_2 - x1_3 = 0;
subject to c2_3:
	-1.0 / x2_3 - (cos(x3_3)) / (1.62079*(0.01+0.3*u3*u3)*(x2_3*x2_3)*x2_3) = 0;
subject to c3_3:
	0.00437*u3 / ((0.01+0.3*u3*u3) * (x2_3*x2_3) )  - 0.00437*(cos(x3_3)) / (1.62079*(0.01+0.3*u3*u3)*(x2_3*x2_3)*x2_3*x2_3) + 0.1*x3_2 - 0.1*x3_3 = 0;
subject to c1_4:
	0.00437*(cos(x3_4)) / (1.62079*(0.01+0.3*u4*u4)*x2_4*x2_4) + x1_3 - x1_4 = 0;
subject to c2_4:
	-1.0 / x2_4 - (cos(x3_4)) / (1.62079*(0.01+0.3*u4*u4)*(x2_4*x2_4)*x2_4) = 0;
subject to c3_4:
	0.00437*u4 / ((0.01+0.3*u4*u4) * (x2_4*x2_4) )  - 0.00437*(cos(x3_4)) / (1.62079*(0.01+0.3*u4*u4)*(x2_4*x2_4)*x2_4*x2_4) + 0.1*x3_3 - 0.1*x3_4 = 0;
subject to c1_5:
	0.00437*(cos(x3_5)) / (1.62079*(0.01+0.3*u5*u5)*x2_5*x2_5) + x1_4 - x1_5 = 0;
subject to c2_5:
	-1.0 / x2_5 - (cos(x3_5)) / (1.62079*(0.01+0.3*u5*u5)*(x2_5*x2_5)*x2_5) = 0;
subject to c3_5:
	0.00437*u5 / ((0.01+0.3*u5*u5) * (x2_5*x2_5) )  - 0.00437*(cos(x3_5)) / (1.62079*(0.01+0.3*u5*u5)*(x2_5*x2_5)*x2_5*x2_5) + 0.1*x3_4 - 0.1*x3_5 = 0;
subject to c1_6:
	0.00437*(cos(x3_6)) / (1.62079*(0.01+0.3*u6*u6)*x2_6*x2_6) + x1_5 - x1_6 = 0;
subject to c2_6:
	-1.0 / x2_6 - (cos(x3_6)) / (1.62079*(0.01+0.3*u6*u6)*(x2_6*x2_6)*x2_6) = 0;
subject to c3_6:
	0.00437*u6 / ((0.01+0.3*u6*u6) * (x2_6*x2_6) )  - 0.00437*(cos(x3_6)) / (1.62079*(0.01+0.3*u6*u6)*(x2_6*x2_6)*x2_6*x2_6) + 0.1*x3_5 - 0.1*x3_6 = 0;
subject to c1_7:
	0.00437*(cos(x3_7)) / (1.62079*(0.01+0.3*u7*u7)*x2_7*x2_7) + x1_6 - x1_7 = 0;
subject to c2_7:
	-1.0 / x2_7 - (cos(x3_7)) / (1.62079*(0.01+0.3*u7*u7)*(x2_7*x2_7)*x2_7) = 0;
subject to c3_7:
	0.00437*u7 / ((0.01+0.3*u7*u7) * (x2_7*x2_7) )  - 0.00437*(cos(x3_7)) / (1.62079*(0.01+0.3*u7*u7)*(x2_7*x2_7)*x2_7*x2_7) + 0.1*x3_6 - 0.1*x3_7 = 0;
subject to c1_8:
	0.00437*(cos(x3_8)) / (1.62079*(0.01+0.3*u8*u8)*x2_8*x2_8) + x1_7 - x1_8 = 0;
subject to c2_8:
	-1.0 / x2_8 - (cos(x3_8)) / (1.62079*(0.01+0.3*u8*u8)*(x2_8*x2_8)*x2_8) = 0;
subject to c3_8:
	0.00437*u8 / ((0.01+0.3*u8*u8) * (x2_8*x2_8) )  - 0.00437*(cos(x3_8)) / (1.62079*(0.01+0.3*u8*u8)*(x2_8*x2_8)*x2_8*x2_8) + 0.1*x3_7 - 0.1*x3_8 = 0;
subject to c1_9:
	0.00437*(cos(x3_9)) / (1.62079*(0.01+0.3*u9*u9)*x2_9*x2_9) + x1_8 - x1_9 = 0;
subject to c2_9:
	-1.0 / x2_9 - (cos(x3_9)) / (1.62079*(0.01+0.3*u9*u9)*(x2_9*x2_9)*x2_9) = 0;
subject to c3_9:
	0.00437*u9 / ((0.01+0.3*u9*u9) * (x2_9*x2_9) )  - 0.00437*(cos(x3_9)) / (1.62079*(0.01+0.3*u9*u9)*(x2_9*x2_9)*x2_9*x2_9) + 0.1*x3_8 - 0.1*x3_9 = 0;
subject to c1_10:
	0.00437*(cos(x3_10)) / (1.62079*(0.01+0.3*u10*u10)*x2_10*x2_10) + x1_9 - x1_10 = 0;
subject to c2_10:
	-1.0 / x2_10 - (cos(x3_10)) / (1.62079*(0.01+0.3*u10*u10)*(x2_10*x2_10)*x2_10) = 0;
subject to c3_10:
	0.00437*u10 / ((0.01+0.3*u10*u10) * (x2_10*x2_10) )  - 0.00437*(cos(x3_10)) / (1.62079*(0.01+0.3*u10*u10)*(x2_10*x2_10)*x2_10*x2_10) + 0.1*x3_9 - 0.1*x3_10 = 0;
subject to c1_11:
	0.00437*(cos(x3_11)) / (1.62079*(0.01+0.3*u11*u11)*x2_11*x2_11) + x1_10 - x1_11 = 0;
subject to c2_11:
	-1.0 / x2_11 - (cos(x3_11)) / (1.62079*(0.01+0.3*u11*u11)*(x2_11*x2_11)*x2_11) = 0;
subject to c3_11:
	0.00437*u11 / ((0.01+0.3*u11*u11) * (x2_11*x2_11) )  - 0.00437*(cos(x3_11)) / (1.62079*(0.01+0.3*u11*u11)*(x2_11*x2_11)*x2_11*x2_11) + 0.1*x3_10 - 0.1*x3_11 = 0;
subject to c1_12:
	0.00437*(cos(x3_12)) / (1.62079*(0.01+0.3*u12*u12)*x2_12*x2_12) + x1_11 - x1_12 = 0;
subject to c2_12:
	-1.0 / x2_12 - (cos(x3_12)) / (1.62079*(0.01+0.3*u12*u12)*(x2_12*x2_12)*x2_12) = 0;
subject to c3_12:
	0.00437*u12 / ((0.01+0.3*u12*u12) * (x2_12*x2_12) )  - 0.00437*(cos(x3_12)) / (1.62079*(0.01+0.3*u12*u12)*(x2_12*x2_12)*x2_12*x2_12) + 0.1*x3_11 - 0.1*x3_12 = 0;
subject to c1_13:
	0.00437*(cos(x3_13)) / (1.62079*(0.01+0.3*u13*u13)*x2_13*x2_13) + x1_12 - x1_13 = 0;
subject to c2_13:
	-1.0 / x2_13 - (cos(x3_13)) / (1.62079*(0.01+0.3*u13*u13)*(x2_13*x2_13)*x2_13) = 0;
subject to c3_13:
	0.00437*u13 / ((0.01+0.3*u13*u13) * (x2_13*x2_13) )  - 0.00437*(cos(x3_13)) / (1.62079*(0.01+0.3*u13*u13)*(x2_13*x2_13)*x2_13*x2_13) + 0.1*x3_12 - 0.1*x3_13 = 0;
subject to c1_14:
	0.00437*(cos(x3_14)) / (1.62079*(0.01+0.3*u14*u14)*x2_14*x2_14) + x1_13 - x1_14 = 0;
subject to c2_14:
	-1.0 / x2_14 - (cos(x3_14)) / (1.62079*(0.01+0.3*u14*u14)*(x2_14*x2_14)*x2_14) = 0;
subject to c3_14:
	0.00437*u14 / ((0.01+0.3*u14*u14) * (x2_14*x2_14) )  - 0.00437*(cos(x3_14)) / (1.62079*(0.01+0.3*u14*u14)*(x2_14*x2_14)*x2_14*x2_14) + 0.1*x3_13 - 0.1*x3_14 = 0;
subject to c1_15:
	0.00437*(cos(x3_15)) / (1.62079*(0.01+0.3*u15*u15)*x2_15*x2_15) + x1_14 - x1_15 = 0;
subject to c2_15:
	-1.0 / x2_15 - (cos(x3_15)) / (1.62079*(0.01+0.3*u15*u15)*(x2_15*x2_15)*x2_15) = 0;
subject to c3_15:
	0.00437*u15 / ((0.01+0.3*u15*u15) * (x2_15*x2_15) )  - 0.00437*(cos(x3_15)) / (1.62079*(0.01+0.3*u15*u15)*(x2_15*x2_15)*x2_15*x2_15) + 0.1*x3_14 - 0.1*x3_15 = 0;
subject to c1_16:
	0.00437*(cos(x3_16)) / (1.62079*(0.01+0.3*u16*u16)*x2_16*x2_16) + x1_15 - x1_16 = 0;
subject to c2_16:
	-1.0 / x2_16 - (cos(x3_16)) / (1.62079*(0.01+0.3*u16*u16)*(x2_16*x2_16)*x2_16) = 0;
subject to c3_16:
	0.00437*u16 / ((0.01+0.3*u16*u16) * (x2_16*x2_16) )  - 0.00437*(cos(x3_16)) / (1.62079*(0.01+0.3*u16*u16)*(x2_16*x2_16)*x2_16*x2_16) + 0.1*x3_15 - 0.1*x3_16 = 0;
subject to c1_17:
	0.00437*(cos(x3_17)) / (1.62079*(0.01+0.3*u17*u17)*x2_17*x2_17) + x1_16 - x1_17 = 0;
subject to c2_17:
	-1.0 / x2_17 - (cos(x3_17)) / (1.62079*(0.01+0.3*u17*u17)*(x2_17*x2_17)*x2_17) = 0;
subject to c3_17:
	0.00437*u17 / ((0.01+0.3*u17*u17) * (x2_17*x2_17) )  - 0.00437*(cos(x3_17)) / (1.62079*(0.01+0.3*u17*u17)*(x2_17*x2_17)*x2_17*x2_17) + 0.1*x3_16 - 0.1*x3_17 = 0;
subject to c1_18:
	0.00437*(cos(x3_18)) / (1.62079*(0.01+0.3*u18*u18)*x2_18*x2_18) + x1_17 - x1_18 = 0;
subject to c2_18:
	-1.0 / x2_18 - (cos(x3_18)) / (1.62079*(0.01+0.3*u18*u18)*(x2_18*x2_18)*x2_18) = 0;
subject to c3_18:
	0.00437*u18 / ((0.01+0.3*u18*u18) * (x2_18*x2_18) )  - 0.00437*(cos(x3_18)) / (1.62079*(0.01+0.3*u18*u18)*(x2_18*x2_18)*x2_18*x2_18) + 0.1*x3_17 - 0.1*x3_18 = 0;
subject to c1_19:
	0.00437*(cos(x3_19)) / (1.62079*(0.01+0.3*u19*u19)*x2_19*x2_19) + x1_18 - x1_19 = 0;
subject to c2_19:
	-1.0 / x2_19 - (cos(x3_19)) / (1.62079*(0.01+0.3*u19*u19)*(x2_19*x2_19)*x2_19) = 0;
subject to c3_19:
	0.00437*u19 / ((0.01+0.3*u19*u19) * (x2_19*x2_19) )  - 0.00437*(cos(x3_19)) / (1.62079*(0.01+0.3*u19*u19)*(x2_19*x2_19)*x2_19*x2_19) + 0.1*x3_18 - 0.1*x3_19 = 0;
subject to c1_20:
	0.00437*(cos(x3_20)) / (1.62079*(0.01+0.3*u20*u20)*x2_20*x2_20) + x1_19 - x1_20 = 0;
subject to c2_20:
	-1.0 / x2_20 - (cos(x3_20)) / (1.62079*(0.01+0.3*u20*u20)*(x2_20*x2_20)*x2_20) = 0;
subject to c3_20:
	0.00437*u20 / ((0.01+0.3*u20*u20) * (x2_20*x2_20) )  - 0.00437*(cos(x3_20)) / (1.62079*(0.01+0.3*u20*u20)*(x2_20*x2_20)*x2_20*x2_20) + 0.1*x3_19 - 0.1*x3_20 = 0;
subject to c1_21:
	0.00437*(cos(x3_21)) / (1.62079*(0.01+0.3*u21*u21)*x2_21*x2_21) + x1_20 - x1_21 = 0;
subject to c2_21:
	-1.0 / x2_21 - (cos(x3_21)) / (1.62079*(0.01+0.3*u21*u21)*(x2_21*x2_21)*x2_21) = 0;
subject to c3_21:
	0.00437*u21 / ((0.01+0.3*u21*u21) * (x2_21*x2_21) )  - 0.00437*(cos(x3_21)) / (1.62079*(0.01+0.3*u21*u21)*(x2_21*x2_21)*x2_21*x2_21) + 0.1*x3_20 - 0.1*x3_21 = 0;
subject to c1_22:
	0.00437*(cos(x3_22)) / (1.62079*(0.01+0.3*u22*u22)*x2_22*x2_22) + x1_21 - x1_22 = 0;
subject to c2_22:
	-1.0 / x2_22 - (cos(x3_22)) / (1.62079*(0.01+0.3*u22*u22)*(x2_22*x2_22)*x2_22) = 0;
subject to c3_22:
	0.00437*u22 / ((0.01+0.3*u22*u22) * (x2_22*x2_22) )  - 0.00437*(cos(x3_22)) / (1.62079*(0.01+0.3*u22*u22)*(x2_22*x2_22)*x2_22*x2_22) + 0.1*x3_21 - 0.1*x3_22 = 0;
subject to c1_23:
	0.00437*(cos(x3_23)) / (1.62079*(0.01+0.3*u23*u23)*x2_23*x2_23) + x1_22 - x1_23 = 0;
subject to c2_23:
	-1.0 / x2_23 - (cos(x3_23)) / (1.62079*(0.01+0.3*u23*u23)*(x2_23*x2_23)*x2_23) = 0;
subject to c3_23:
	0.00437*u23 / ((0.01+0.3*u23*u23) * (x2_23*x2_23) )  - 0.00437*(cos(x3_23)) / (1.62079*(0.01+0.3*u23*u23)*(x2_23*x2_23)*x2_23*x2_23) + 0.1*x3_22 - 0.1*x3_23 = 0;
subject to c1_24:
	0.00437*(cos(x3_24)) / (1.62079*(0.01+0.3*u24*u24)*x2_24*x2_24) + x1_23 - x1_24 = 0;
subject to c2_24:
	-1.0 / x2_24 - (cos(x3_24)) / (1.62079*(0.01+0.3*u24*u24)*(x2_24*x2_24)*x2_24) = 0;
subject to c3_24:
	0.00437*u24 / ((0.01+0.3*u24*u24) * (x2_24*x2_24) )  - 0.00437*(cos(x3_24)) / (1.62079*(0.01+0.3*u24*u24)*(x2_24*x2_24)*x2_24*x2_24) + 0.1*x3_23 - 0.1*x3_24 = 0;
subject to c1_25:
	0.00437*(cos(x3_25)) / (1.62079*(0.01+0.3*u25*u25)*x2_25*x2_25) + x1_24 - x1_25 = 0;
subject to c2_25:
	-1.0 / x2_25 - (cos(x3_25)) / (1.62079*(0.01+0.3*u25*u25)*(x2_25*x2_25)*x2_25) = 0;
subject to c3_25:
	0.00437*u25 / ((0.01+0.3*u25*u25) * (x2_25*x2_25) )  - 0.00437*(cos(x3_25)) / (1.62079*(0.01+0.3*u25*u25)*(x2_25*x2_25)*x2_25*x2_25) + 0.1*x3_24 - 0.1*x3_25 = 0;
subject to c1_26:
	0.00437*(cos(x3_26)) / (1.62079*(0.01+0.3*u26*u26)*x2_26*x2_26) + x1_25 - x1_26 = 0;
subject to c2_26:
	-1.0 / x2_26 - (cos(x3_26)) / (1.62079*(0.01+0.3*u26*u26)*(x2_26*x2_26)*x2_26) = 0;
subject to c3_26:
	0.00437*u26 / ((0.01+0.3*u26*u26) * (x2_26*x2_26) )  - 0.00437*(cos(x3_26)) / (1.62079*(0.01+0.3*u26*u26)*(x2_26*x2_26)*x2_26*x2_26) + 0.1*x3_25 - 0.1*x3_26 = 0;
subject to c1_27:
	0.00437*(cos(x3_27)) / (1.62079*(0.01+0.3*u27*u27)*x2_27*x2_27) + x1_26 - x1_27 = 0;
subject to c2_27:
	-1.0 / x2_27 - (cos(x3_27)) / (1.62079*(0.01+0.3*u27*u27)*(x2_27*x2_27)*x2_27) = 0;
subject to c3_27:
	0.00437*u27 / ((0.01+0.3*u27*u27) * (x2_27*x2_27) )  - 0.00437*(cos(x3_27)) / (1.62079*(0.01+0.3*u27*u27)*(x2_27*x2_27)*x2_27*x2_27) + 0.1*x3_26 - 0.1*x3_27 = 0;
subject to c1_28:
	0.00437*(cos(x3_28)) / (1.62079*(0.01+0.3*u28*u28)*x2_28*x2_28) + x1_27 - x1_28 = 0;
subject to c2_28:
	-1.0 / x2_28 - (cos(x3_28)) / (1.62079*(0.01+0.3*u28*u28)*(x2_28*x2_28)*x2_28) = 0;
subject to c3_28:
	0.00437*u28 / ((0.01+0.3*u28*u28) * (x2_28*x2_28) )  - 0.00437*(cos(x3_28)) / (1.62079*(0.01+0.3*u28*u28)*(x2_28*x2_28)*x2_28*x2_28) + 0.1*x3_27 - 0.1*x3_28 = 0;
subject to c1_29:
	0.00437*(cos(x3_29)) / (1.62079*(0.01+0.3*u29*u29)*x2_29*x2_29) + x1_28 - x1_29 = 0;
subject to c2_29:
	-1.0 / x2_29 - (cos(x3_29)) / (1.62079*(0.01+0.3*u29*u29)*(x2_29*x2_29)*x2_29) = 0;
subject to c3_29:
	0.00437*u29 / ((0.01+0.3*u29*u29) * (x2_29*x2_29) )  - 0.00437*(cos(x3_29)) / (1.62079*(0.01+0.3*u29*u29)*(x2_29*x2_29)*x2_29*x2_29) + 0.1*x3_28 - 0.1*x3_29 = 0;
subject to c1_30:
	0.00437*(cos(x3_30)) / (1.62079*(0.01+0.3*u30*u30)*x2_30*x2_30) + x1_29 - x1_30 = 0;
subject to c2_30:
	-1.0 / x2_30 - (cos(x3_30)) / (1.62079*(0.01+0.3*u30*u30)*(x2_30*x2_30)*x2_30) = 0;
subject to c3_30:
	0.00437*u30 / ((0.01+0.3*u30*u30) * (x2_30*x2_30) )  - 0.00437*(cos(x3_30)) / (1.62079*(0.01+0.3*u30*u30)*(x2_30*x2_30)*x2_30*x2_30) + 0.1*x3_29 - 0.1*x3_30 = 0;
subject to c1_31:
	0.00437*(cos(x3_31)) / (1.62079*(0.01+0.3*u31*u31)*x2_31*x2_31) + x1_30 - x1_31 = 0;
subject to c2_31:
	-1.0 / x2_31 - (cos(x3_31)) / (1.62079*(0.01+0.3*u31*u31)*(x2_31*x2_31)*x2_31) = 0;
subject to c3_31:
	0.00437*u31 / ((0.01+0.3*u31*u31) * (x2_31*x2_31) )  - 0.00437*(cos(x3_31)) / (1.62079*(0.01+0.3*u31*u31)*(x2_31*x2_31)*x2_31*x2_31) + 0.1*x3_30 - 0.1*x3_31 = 0;
subject to c1_32:
	0.00437*(cos(x3_32)) / (1.62079*(0.01+0.3*u32*u32)*x2_32*x2_32) + x1_31 - x1_32 = 0;
subject to c2_32:
	-1.0 / x2_32 - (cos(x3_32)) / (1.62079*(0.01+0.3*u32*u32)*(x2_32*x2_32)*x2_32) = 0;
subject to c3_32:
	0.00437*u32 / ((0.01+0.3*u32*u32) * (x2_32*x2_32) )  - 0.00437*(cos(x3_32)) / (1.62079*(0.01+0.3*u32*u32)*(x2_32*x2_32)*x2_32*x2_32) + 0.1*x3_31 - 0.1*x3_32 = 0;
subject to c1_33:
	0.00437*(cos(x3_33)) / (1.62079*(0.01+0.3*u33*u33)*x2_33*x2_33) + x1_32 - x1_33 = 0;
subject to c2_33:
	-1.0 / x2_33 - (cos(x3_33)) / (1.62079*(0.01+0.3*u33*u33)*(x2_33*x2_33)*x2_33) = 0;
subject to c3_33:
	0.00437*u33 / ((0.01+0.3*u33*u33) * (x2_33*x2_33) )  - 0.00437*(cos(x3_33)) / (1.62079*(0.01+0.3*u33*u33)*(x2_33*x2_33)*x2_33*x2_33) + 0.1*x3_32 - 0.1*x3_33 = 0;
subject to c1_34:
	0.00437*(cos(x3_34)) / (1.62079*(0.01+0.3*u34*u34)*x2_34*x2_34) + x1_33 - x1_34 = 0;
subject to c2_34:
	-1.0 / x2_34 - (cos(x3_34)) / (1.62079*(0.01+0.3*u34*u34)*(x2_34*x2_34)*x2_34) = 0;
subject to c3_34:
	0.00437*u34 / ((0.01+0.3*u34*u34) * (x2_34*x2_34) )  - 0.00437*(cos(x3_34)) / (1.62079*(0.01+0.3*u34*u34)*(x2_34*x2_34)*x2_34*x2_34) + 0.1*x3_33 - 0.1*x3_34 = 0;
subject to c1_35:
	0.00437*(cos(x3_35)) / (1.62079*(0.01+0.3*u35*u35)*x2_35*x2_35) + x1_34 - x1_35 = 0;
subject to c2_35:
	-1.0 / x2_35 - (cos(x3_35)) / (1.62079*(0.01+0.3*u35*u35)*(x2_35*x2_35)*x2_35) = 0;
subject to c3_35:
	0.00437*u35 / ((0.01+0.3*u35*u35) * (x2_35*x2_35) )  - 0.00437*(cos(x3_35)) / (1.62079*(0.01+0.3*u35*u35)*(x2_35*x2_35)*x2_35*x2_35) + 0.1*x3_34 - 0.1*x3_35 = 0;
subject to c1_36:
	0.00437*(cos(x3_36)) / (1.62079*(0.01+0.3*u36*u36)*x2_36*x2_36) + x1_35 - x1_36 = 0;
subject to c2_36:
	-1.0 / x2_36 - (cos(x3_36)) / (1.62079*(0.01+0.3*u36*u36)*(x2_36*x2_36)*x2_36) = 0;
subject to c3_36:
	0.00437*u36 / ((0.01+0.3*u36*u36) * (x2_36*x2_36) )  - 0.00437*(cos(x3_36)) / (1.62079*(0.01+0.3*u36*u36)*(x2_36*x2_36)*x2_36*x2_36) + 0.1*x3_35 - 0.1*x3_36 = 0;
subject to c1_37:
	0.00437*(cos(x3_37)) / (1.62079*(0.01+0.3*u37*u37)*x2_37*x2_37) + x1_36 - x1_37 = 0;
subject to c2_37:
	-1.0 / x2_37 - (cos(x3_37)) / (1.62079*(0.01+0.3*u37*u37)*(x2_37*x2_37)*x2_37) = 0;
subject to c3_37:
	0.00437*u37 / ((0.01+0.3*u37*u37) * (x2_37*x2_37) )  - 0.00437*(cos(x3_37)) / (1.62079*(0.01+0.3*u37*u37)*(x2_37*x2_37)*x2_37*x2_37) + 0.1*x3_36 - 0.1*x3_37 = 0;
subject to c1_38:
	0.00437*(cos(x3_38)) / (1.62079*(0.01+0.3*u38*u38)*x2_38*x2_38) + x1_37 - x1_38 = 0;
subject to c2_38:
	-1.0 / x2_38 - (cos(x3_38)) / (1.62079*(0.01+0.3*u38*u38)*(x2_38*x2_38)*x2_38) = 0;
subject to c3_38:
	0.00437*u38 / ((0.01+0.3*u38*u38) * (x2_38*x2_38) )  - 0.00437*(cos(x3_38)) / (1.62079*(0.01+0.3*u38*u38)*(x2_38*x2_38)*x2_38*x2_38) + 0.1*x3_37 - 0.1*x3_38 = 0;
subject to c1_39:
	0.00437*(cos(x3_39)) / (1.62079*(0.01+0.3*u39*u39)*x2_39*x2_39) + x1_38 - x1_39 = 0;
subject to c2_39:
	-1.0 / x2_39 - (cos(x3_39)) / (1.62079*(0.01+0.3*u39*u39)*(x2_39*x2_39)*x2_39) = 0;
subject to c3_39:
	0.00437*u39 / ((0.01+0.3*u39*u39) * (x2_39*x2_39) )  - 0.00437*(cos(x3_39)) / (1.62079*(0.01+0.3*u39*u39)*(x2_39*x2_39)*x2_39*x2_39) + 0.1*x3_38 - 0.1*x3_39 = 0;
subject to c1_40:
	0.00437*(cos(x3_40)) / (1.62079*(0.01+0.3*u40*u40)*x2_40*x2_40) + x1_39 - x1_40 = 0;
subject to c2_40:
	-1.0 / x2_40 - (cos(x3_40)) / (1.62079*(0.01+0.3*u40*u40)*(x2_40*x2_40)*x2_40) = 0;
subject to c3_40:
	0.00437*u40 / ((0.01+0.3*u40*u40) * (x2_40*x2_40) )  - 0.00437*(cos(x3_40)) / (1.62079*(0.01+0.3*u40*u40)*(x2_40*x2_40)*x2_40*x2_40) + 0.1*x3_39 - 0.1*x3_40 = 0;
subject to c1_41:
	0.00437*(cos(x3_41)) / (1.62079*(0.01+0.3*u41*u41)*x2_41*x2_41) + x1_40 - x1_41 = 0;
subject to c2_41:
	-1.0 / x2_41 - (cos(x3_41)) / (1.62079*(0.01+0.3*u41*u41)*(x2_41*x2_41)*x2_41) = 0;
subject to c3_41:
	0.00437*u41 / ((0.01+0.3*u41*u41) * (x2_41*x2_41) )  - 0.00437*(cos(x3_41)) / (1.62079*(0.01+0.3*u41*u41)*(x2_41*x2_41)*x2_41*x2_41) + 0.1*x3_40 - 0.1*x3_41 = 0;
subject to c1_42:
	0.00437*(cos(x3_42)) / (1.62079*(0.01+0.3*u42*u42)*x2_42*x2_42) + x1_41 - x1_42 = 0;
subject to c2_42:
	-1.0 / x2_42 - (cos(x3_42)) / (1.62079*(0.01+0.3*u42*u42)*(x2_42*x2_42)*x2_42) = 0;
subject to c3_42:
	0.00437*u42 / ((0.01+0.3*u42*u42) * (x2_42*x2_42) )  - 0.00437*(cos(x3_42)) / (1.62079*(0.01+0.3*u42*u42)*(x2_42*x2_42)*x2_42*x2_42) + 0.1*x3_41 - 0.1*x3_42 = 0;
subject to c1_43:
	0.00437*(cos(x3_43)) / (1.62079*(0.01+0.3*u43*u43)*x2_43*x2_43) + x1_42 - x1_43 = 0;
subject to c2_43:
	-1.0 / x2_43 - (cos(x3_43)) / (1.62079*(0.01+0.3*u43*u43)*(x2_43*x2_43)*x2_43) = 0;
subject to c3_43:
	0.00437*u43 / ((0.01+0.3*u43*u43) * (x2_43*x2_43) )  - 0.00437*(cos(x3_43)) / (1.62079*(0.01+0.3*u43*u43)*(x2_43*x2_43)*x2_43*x2_43) + 0.1*x3_42 - 0.1*x3_43 = 0;
subject to c1_44:
	0.00437*(cos(x3_44)) / (1.62079*(0.01+0.3*u44*u44)*x2_44*x2_44) + x1_43 - x1_44 = 0;
subject to c2_44:
	-1.0 / x2_44 - (cos(x3_44)) / (1.62079*(0.01+0.3*u44*u44)*(x2_44*x2_44)*x2_44) = 0;
subject to c3_44:
	0.00437*u44 / ((0.01+0.3*u44*u44) * (x2_44*x2_44) )  - 0.00437*(cos(x3_44)) / (1.62079*(0.01+0.3*u44*u44)*(x2_44*x2_44)*x2_44*x2_44) + 0.1*x3_43 - 0.1*x3_44 = 0;
subject to c1_45:
	0.00437*(cos(x3_45)) / (1.62079*(0.01+0.3*u45*u45)*x2_45*x2_45) + x1_44 - x1_45 = 0;
subject to c2_45:
	-1.0 / x2_45 - (cos(x3_45)) / (1.62079*(0.01+0.3*u45*u45)*(x2_45*x2_45)*x2_45) = 0;
subject to c3_45:
	0.00437*u45 / ((0.01+0.3*u45*u45) * (x2_45*x2_45) )  - 0.00437*(cos(x3_45)) / (1.62079*(0.01+0.3*u45*u45)*(x2_45*x2_45)*x2_45*x2_45) + 0.1*x3_44 - 0.1*x3_45 = 0;
subject to c1_46:
	0.00437*(cos(x3_46)) / (1.62079*(0.01+0.3*u46*u46)*x2_46*x2_46) + x1_45 - x1_46 = 0;
subject to c2_46:
	-1.0 / x2_46 - (cos(x3_46)) / (1.62079*(0.01+0.3*u46*u46)*(x2_46*x2_46)*x2_46) = 0;
subject to c3_46:
	0.00437*u46 / ((0.01+0.3*u46*u46) * (x2_46*x2_46) )  - 0.00437*(cos(x3_46)) / (1.62079*(0.01+0.3*u46*u46)*(x2_46*x2_46)*x2_46*x2_46) + 0.1*x3_45 - 0.1*x3_46 = 0;
subject to c1_47:
	0.00437*(cos(x3_47)) / (1.62079*(0.01+0.3*u47*u47)*x2_47*x2_47) + x1_46 - x1_47 = 0;
subject to c2_47:
	-1.0 / x2_47 - (cos(x3_47)) / (1.62079*(0.01+0.3*u47*u47)*(x2_47*x2_47)*x2_47) = 0;
subject to c3_47:
	0.00437*u47 / ((0.01+0.3*u47*u47) * (x2_47*x2_47) )  - 0.00437*(cos(x3_47)) / (1.62079*(0.01+0.3*u47*u47)*(x2_47*x2_47)*x2_47*x2_47) + 0.1*x3_46 - 0.1*x3_47 = 0;
subject to c1_48:
	0.00437*(cos(x3_48)) / (1.62079*(0.01+0.3*u48*u48)*x2_48*x2_48) + x1_47 - x1_48 = 0;
subject to c2_48:
	-1.0 / x2_48 - (cos(x3_48)) / (1.62079*(0.01+0.3*u48*u48)*(x2_48*x2_48)*x2_48) = 0;
subject to c3_48:
	0.00437*u48 / ((0.01+0.3*u48*u48) * (x2_48*x2_48) )  - 0.00437*(cos(x3_48)) / (1.62079*(0.01+0.3*u48*u48)*(x2_48*x2_48)*x2_48*x2_48) + 0.1*x3_47 - 0.1*x3_48 = 0;
subject to c1_49:
	0.00437*(cos(x3_49)) / (1.62079*(0.01+0.3*u49*u49)*x2_49*x2_49) + x1_48 - x1_49 = 0;
subject to c2_49:
	-1.0 / x2_49 - (cos(x3_49)) / (1.62079*(0.01+0.3*u49*u49)*(x2_49*x2_49)*x2_49) = 0;
subject to c3_49:
	0.00437*u49 / ((0.01+0.3*u49*u49) * (x2_49*x2_49) )  - 0.00437*(cos(x3_49)) / (1.62079*(0.01+0.3*u49*u49)*(x2_49*x2_49)*x2_49*x2_49) + 0.1*x3_48 - 0.1*x3_49 = 0;
subject to c1_50:
	0.00437*(cos(x3_50)) / (1.62079*(0.01+0.3*u50*u50)*x2_50*x2_50) + x1_49 - x1_50 = 0;
subject to c2_50:
	-1.0 / x2_50 - (cos(x3_50)) / (1.62079*(0.01+0.3*u50*u50)*(x2_50*x2_50)*x2_50) = 0;
subject to c3_50:
	0.00437*u50 / ((0.01+0.3*u50*u50) * (x2_50*x2_50) )  - 0.00437*(cos(x3_50)) / (1.62079*(0.01+0.3*u50*u50)*(x2_50*x2_50)*x2_50*x2_50) + 0.1*x3_49 - 0.1*x3_50 = 0;

solve;
display x1_0;
display x2_0;
display x3_0;
display x1_1;
display x2_1;
display x3_1;
display x1_2;
display x2_2;
display x3_2;
display x1_3;
display x2_3;
display x3_3;
display x1_4;
display x2_4;
display x3_4;
display x1_5;
display x2_5;
display x3_5;
display x1_6;
display x2_6;
display x3_6;
display x1_7;
display x2_7;
display x3_7;
display x1_8;
display x2_8;
display x3_8;
display x1_9;
display x2_9;
display x3_9;
display x1_10;
display x2_10;
display x3_10;
display x1_11;
display x2_11;
display x3_11;
display x1_12;
display x2_12;
display x3_12;
display x1_13;
display x2_13;
display x3_13;
display x1_14;
display x2_14;
display x3_14;
display x1_15;
display x2_15;
display x3_15;
display x1_16;
display x2_16;
display x3_16;
display x1_17;
display x2_17;
display x3_17;
display x1_18;
display x2_18;
display x3_18;
display x1_19;
display x2_19;
display x3_19;
display x1_20;
display x2_20;
display x3_20;
display x1_21;
display x2_21;
display x3_21;
display x1_22;
display x2_22;
display x3_22;
display x1_23;
display x2_23;
display x3_23;
display x1_24;
display x2_24;
display x3_24;
display x1_25;
display x2_25;
display x3_25;
display x1_26;
display x2_26;
display x3_26;
display x1_27;
display x2_27;
display x3_27;
display x1_28;
display x2_28;
display x3_28;
display x1_29;
display x2_29;
display x3_29;
display x1_30;
display x2_30;
display x3_30;
display x1_31;
display x2_31;
display x3_31;
display x1_32;
display x2_32;
display x3_32;
display x1_33;
display x2_33;
display x3_33;
display x1_34;
display x2_34;
display x3_34;
display x1_35;
display x2_35;
display x3_35;
display x1_36;
display x2_36;
display x3_36;
display x1_37;
display x2_37;
display x3_37;
display x1_38;
display x2_38;
display x3_38;
display x1_39;
display x2_39;
display x3_39;
display x1_40;
display x2_40;
display x3_40;
display x1_41;
display x2_41;
display x3_41;
display x1_42;
display x2_42;
display x3_42;
display x1_43;
display x2_43;
display x3_43;
display x1_44;
display x2_44;
display x3_44;
display x1_45;
display x2_45;
display x3_45;
display x1_46;
display x2_46;
display x3_46;
display x1_47;
display x2_47;
display x3_47;
display x1_48;
display x2_48;
display x3_48;
display x1_49;
display x2_49;
display x3_49;
display x1_50;
display x2_50;
display x3_50;
display u0;
display u1;
display u2;
display u3;
display u4;
display u5;
display u6;
display u7;
display u8;
display u9;
display u10;
display u11;
display u12;
display u13;
display u14;
display u15;
display u16;
display u17;
display u18;
display u19;
display u20;
display u21;
display u22;
display u23;
display u24;
display u25;
display u26;
display u27;
display u28;
display u29;
display u30;
display u31;
display u32;
display u33;
display u34;
display u35;
display u36;
display u37;
display u38;
display u39;
display u40;
display u41;
display u42;
display u43;
display u44;
display u45;
display u46;
display u47;
display u48;
display u49;
display u50;
display obj;