I am try to optimize this system of nonlinear equations which I wrote on the editor as;
function F = myfun (x)
F = [5-x(1)*(6^x(2)*exp(6*x(3))+12^x(2)*exp(12*x(3))+18^x(2)*exp(18*x(3))+24^x(2)*exp(24*x(3))+30^x(2)*exp(30*x(3)))-2*x(1)*x(4)*(6^x(2)*exp(-x(1)*6^x(2)*exp(6*x(3))+(6*x(3)))*(1-x(4)*exp(-x(1)*6^x(2)*exp(6*x(3))))^(-1)+12^x(2)*exp(-x(1)*12^x(2)*exp(12*x(3))+(12*x(3)))*(1-x(4)*exp(-x(1)*12^x(2)*exp(12*x(3))))^(-1)+18^x(2)*exp(-x(1)*18^x(2)*exp(18*x(3))+(18*x(3)))*(1-x(4)*exp(-x(1)*18^x(2)*exp(18*x(3))))^(-1)+24^x(2)*exp(-x(1)*24^x(2)*exp(24*x(3))+(24*x(3)))*(1-x(4)*exp(-x(1)*24^x(2)*exp(24*x(3))))^(-1)+30^x(2)*exp(-x(1)*30^x(2)*exp(30*x(3))+(30*x(3)))*(1-x(4)*exp(-x(1)*30^x(2)*exp(30*x(3))))^(-1)); (log(6)+log(12)+log(18)+log(24)+log(30))+((x(2)+6*x(3))^(-1)+(x(2)+12*x(3))^(-1)+(x(2)+18*x(3))^(-1)+(x(2)+24*x(3))^(-1)+(x(2)+30*x(3))^(-1))-x(1)*(6^x(2)*exp(6*x(3))*log(6)+12^x(2)*exp(12*x(3))*log(12)+18^x(2)*exp(18*x(3))*log(18)+24^x(2)*exp(24*x(3))*log(24)+30^x(2)*exp(30*x(3))*log(30))-2*x(2)*x(4)*(6^x(2)*exp(-x(1)*6^x(2)*exp(6*x(3))+(6*x(3)))*log(6)*(1-x(4)*exp(-x(1)*6^x(2)*exp(6*x(3))))^(-1)+12^x(2)*exp(-x(1)*12^x(2)*exp(12*x(3))+(12*x(3)))*log(12)*(1-x(4)*exp(-x(1)*12^x(2)*exp(12*x(3))))^(-1)+18^x(2)*exp(-x(1)*18^x(2)*exp(18*x(3))+(18*x(3)))*log(18)*(1-x(4)*exp(-x(1)*18^x(2)*exp(18*x(3))))^(-1)+24^x(2)*exp(-x(1)*24^x(2)*exp(24*x(3))+(24*x(3)))*log(24)*(1-x(4)*exp(-x(1)*24^x(2)*exp(24*x(3))))^(-1)+30^x(2)*exp(-x(1)*30^x(2)*exp(30*x(3))+(30*x(3)))*log(30)*(1-x(4)*exp(-x(1)*30^x(2)*exp(30*x(3))))^(-1)); (6*(x(2)+6*x(3))^(-1)+12*(x(2)+12*x(3))^(-1)+18*(x(2)+18*x(3))^(-1)+24*(x(2)+24*x(3))^(-1)+30*(x(2)+30*x(3))^(-1))-x(1)*(6^(x(2)+1)*exp(6*x(3))+12^(x(2)+1)*exp(12*x(3))+18^(x(2)+1)*exp(18*x(3))+24^(x(2)+1)*exp(24*x(3))+30^(x(2)+1)*exp(30*x(3)))-(6+12+18+24+30)-2*x(1)*x(4)*(6^(x(2)+1)*exp(-x(1)*6^x(2)*exp(6*x(3))+(6*x(3)))*(1-x(4)*exp(-x(1)*6^x(2)*exp(6*x(3))))^(-1)+12^(x(2)+1)*exp(-x(1)*12^x(2)*exp(12*x(3))+(12*x(3)))*(1-x(4)*exp(-x(1)*12^x(2)*exp(12*x(3))))^(-1)+18^(x(2)+1)*exp(-x(1)*18^x(2)*exp(18*x(3))+(18*x(3)))*(1-x(4)*exp(-x(1)*18^x(2)*exp(18*x(3))))^(-1)+24^(x(2)+1)*exp(-x(1)*24^x(2)*exp(24*x(3))+(24*x(3)))*(1-x(4)*exp(-x(1)*24^x(2)*exp(24*x(3))))^(-1)+30^(x(2)+1)*exp(-x(1)*30^x(2)*exp(30*x(3))+(30*x(3)))*(1-x(4)*exp(-x(1)*30^x(2)*exp(30*x(3))))^(-1)); 5*(1-x(4))^(-1)-2*(exp(-x(1)*6^x(2)*exp(6*x(3)))*(1-x(4)*exp(-x(1)*6^x(2)*exp(6*x(3))))^(-1)+exp(-x(1)*12^x(2)*exp(12*x(3)))*(1-x(4)*exp(-x(1)*12^x(2)*exp(12*x(3))))^(-1)+exp(-x(1)*18^x(2)*exp(18*x(3)))*(1-x(4)*exp(-x(1)*18^x(2)*exp(18*x(3))))^(-1)+exp(-x(1)*24^x(2)*exp(24*x(3)))*(1-x(4)*exp(-x(1)*24^x(2)*exp(24*x(3))))^(-1)+exp(-x(1)*30^x(2)*exp(30*x(3)))*(1-x(4)*exp(-x(1)*30^x(2)*exp(30*x(3))))^(-1))];
Then on the command window, I wrote the following;
x0 = [0.2;0.0002;0.0002;0.00015];% Make a starting guess at the solution
options = optimset ('Display', 'iter');% Option to display output
[x, fval] = fsolve(@ myfun, x0, options)% Call optimizer
The output I got is;
Norm of First-order Trust-region Iteration Func-count f(x) step optimality radius 0 5 5.3979e+008 2.53e+012 1 1 10 1.31841e+008 0.939736 3.15e+011 1 2 15 3.31473e+007 0.571025 4.03e+010 1 3 20 7.93185e+006 0.149714 5.13e+009 1 4 25 1.88669e+006 0.193604 6.88e+008 1 5 30 402793 0.784283 9.53e+007 1 6 35 74592.2 0.643981 1.46e+007 1 7 40 6957.78 1 2.1e+006 1 8 41 6957.78 2.5 2.1e+006 2.5 9 46 5000.79 0.625 1.5e+006 0.625 10 51 66.1601 0.625 1.43e+005 0.625 11 52 66.1601 1.5625 1.43e+005 1.56 12 57 3.77601 0.390625 2.28e+004 0.391 13 58 3.77601 0.976562 2.28e+004 0.977 14 63 2.03707 0.244141 8.23e+003 0.244 15 68 1.71988 0.244141 7.71e+003 0.244 16 73 1.45128 0.244141 6.82e+003 0.244 17 78 1.23647 0.244141 6.04e+003 0.244 18 83 1.06229 0.244141 5.36e+003 0.244 19 88 0.919374 0.244141 4.76e+003 0.244 20 93 0.800762 0.244141 4.23e+003 0.244 21 98 0.701267 0.244141 3.77e+003 0.244 22 103 0.616995 0.244141 3.37e+003 0.244 23 108 0.544989 0.244141 3.01e+003 0.244 24 113 0.482979 0.244141 2.7e+003 0.244 25 118 0.429199 0.244141 2.41e+003 0.244 26 123 0.382263 0.244141 2.17e+003 0.244 27 128 0.341066 0.244141 1.94e+003 0.244 28 133 0.304723 0.244141 1.75e+003 0.244 29 138 0.272515 0.244141 1.57e+003 0.244 30 143 0.243854 0.244141 1.41e+003 0.244 31 148 0.218256 0.244141 1.27e+003 0.244 32 153 0.195318 0.244141 1.14e+003 0.244 33 158 0.174701 0.244141 1.03e+003 0.244 34 163 0.156123 0.244141 922 0.244 35 168 0.139343 0.244141 830 0.244 36 173 0.124156 0.244141 748 0.244 37 178 0.110385 0.244141 674 0.244 38 183 0.097881 0.244141 607 0.244 39 188 0.0865129 0.244141 548 0.244 40 193 0.0761683 0.244141 496 0.244 41 198 0.0667494 0.244141 449 0.244 42 203 0.0581714 0.244141 408 0.244 43 208 0.0503606 0.244141 372 0.244 44 213 0.0432528 0.244141 342 0.244 45 218 0.0367926 0.244141 316 0.244 46 223 0.0309326 0.244141 294 0.244 47 228 0.0256321 0.244141 278 0.244 48 233 0.0208576 0.244141 266 0.244 49 238 0.0165818 0.244141 259 0.244 50 243 0.0127843 0.244141 257 0.244 51 248 0.00945222 0.244141 261 0.244 52 253 0.00658082 0.244141 272 0.244 53 258 0.00417637 0.244141 290 0.244 54 263 0.0022604 0.244141 320 0.244 55 268 0.000880068 0.244141 364 0.244 56 273 0.000140147 0.244141 433 0.244 57 278 6.62466e-007 0.0652966 42.2 0.244 58 283 2.36175e-014 7.1433e-005 0.00804 0.244 59 288 1.63177e-023 3.4157e-008 2.14e-007 0.244Optimization terminated: first-order optimality is less than options.TolFun.x = 2.0909 -0.5152 0.0909 -13.4163fval =
1.0e-011 * 0.0009 -0.0696 -0.3979 -0.0000This differs from the condition imposed; x(1)>0,x(2)>0,x(3)>0,x(4)>0.Please, i need help on my initial values that can actualized this imposed condition. Thank you.
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