added remainig solutions to ex02

exercises/ex02/solutions/fit.mod

+reset;
+
+param n := 82;
+param m := 10;
+
+param yx{1..n,1..2};
+
+data filip_yx.dat;
+#display yx;
+
+var a{i in 0..m}; # coefficients
+
+minimize
+obj: sum{i in 1..n} ( sum{k in 0..m} a[k]*yx[i,2]^k - yx[i,1] )^2;
+
+#option solver gurobi;
+#option solver ipopt;
+#option solver bonmin;
+#option solver minos;
+#option solver loqo;
+#option solver cplex;
+#option solver snopt;
+#option solver couenne;
+option solver conopt;
+
+solve;
+
+display a;
+display obj;

exercises/ex02/solutions/fitodr.mod

+reset;
+
+param n := 82;
+param m := 10;
+
+param yx{1..n,1..2};
+
+data filip_yx.dat;
+#display yx;
+
+var a{0..m}; # coefficients
+var d{1..n}; # x-error
+
+minimize
+obj: sum{i in 1..n} ( ( sum{k in 0..m} a[k]*(yx[i,2]+d[i])^k - yx[i,1] )^2 + d[i]^2 );
+
+#option solver snopt;
+#option solver minos;
+#option solver bonmin;
+#option solver ipopt;
+#option solver couenne;
+#option solver loqo;
+option solver conopt;
+
+solve;
+
+display d;
+display a;
+display obj;

exercises/ex02/solutions/sol02.txt

+|------------------|
+| Solution of ex02 |
+|------------------|
+
+
+
+---
+2.1
+---
+
+J = [ 1 + x_2   , x_1 + 2 x_2 ;
+      2 x_1 - 2 , 2 x_2       ]
+
+J(0,0) = [ 1 , 0 ;
+          -2 , 0 ]
+is singular.
+
+For all solvers, the solution for the x_2 component is inaccurate.
+Using KNITRO and the suggested option, the accuracy is to machine precision.
+
+
+
+---
+2.2
+---
+
+There are at least two solutions, one for the suggested starting guess ( x_i = 1 / n ) and one for x_i = (-1)^i / n
+
+Both solutions have the same objective, i.e. 0.
+
+
+
+---
+2.3
+---
+
+Most of solvers give very bad fits. Only CONOPT gives the same solution as the certified values.
+
+The problem is ill-conditioned, with 9 orders of magnitude between the largest and the smallest coefficients.
+
+
+
+---
+2.4
+---
+
+Orthogonal distance regression improves the solution for most solvers (in that the residuals are smaller), but still CONOPT is the only one getting the same solution as the certified values.
+