added solution to ex09

exercises/ex09/solutions/boiler.mod

+reset;
+
+param n := 5;		# number of variables
+
+set I = {1..5};
+
+param a{I};
+param b{I};
+param c{I};
+param d{I};
+param l{I};
+param u{I};
+
+var x{i in I} >= l[i], <= u[i];
+
+minimize f: 
+	sum{i in I} x[i]/(a[i]+b[i]*x[i]+c[i]*x[i]^2+d[i]*x[i]^3);
+
+s.t. budget: sum{i in I} x[i] = 350;
+
+data;
+
+param:  l u a b c d :=
+1 10    60    56.49  1.67  -0.041  0.00030
+2 10    60    71.37  0.61  -0.016  0.00011
+3 15   120    23.88  2.05  -0.024  0.00009
+4 12.5 112.5  17.14  2.73  -0.035  0.00014
+5 15   135    72.38  0.34  -0.003  0.00001;
+ 
+option solver knitro; 
+option knitro_options "ms_enable=1";
+
+#option solver couenne; 
+
+solve;
+
+display f;
+print{i in 1..n} x[i];

exercises/ex09/solutions/boiler_int1.mod

+reset;
+
+param n := 5;		# number of variables
+
+set I = {1..5};
+
+param a{I};
+param b{I};
+param c{I};
+param d{I};
+param l{I};
+param u{I};
+
+var y{I} binary;
+var x{i in I};
+
+minimize f: 
+	sum{i in I} x[i]/(a[i]+b[i]*x[i]+c[i]*x[i]^2+d[i]*x[i]^3);
+
+s.t. budget: sum{i in I} x[i] = 350;
+s.t. low{i in I}: x[i] >= l[i] * y[i];
+s.t. high{i in I}: x[i] <= u[i] * y[i];
+
+data;
+
+param:  l u a b c d :=
+1 10    60    56.49  1.67  -0.041  0.00030
+2 10    60    71.37  0.61  -0.016  0.00011
+3 15   120    23.88  2.05  -0.024  0.00009
+4 12.5 112.5  17.14  2.73  -0.035  0.00014
+5 15   135    72.38  0.34  -0.003  0.00001;
+ 
+#option solver knitro; 
+#option knitro_options "ms_enable=1";
+
+option solver couenne; 
+
+solve;
+
+display f;
+print{i in 1..n} x[i];
+print{i in 1..n} y[i];
+

exercises/ex09/solutions/boiler_int2.mod

+reset;
+
+param n := 5;		# number of variables
+
+set I = {1..5};
+
+param a{I};
+param b{I};
+param c{I};
+param d{I};
+param l{I};
+param u{I};
+
+var x{i in I} >= l[i], <= u[i];
+var y{I} binary;
+
+minimize f: 
+	sum{i in I} y[i]*x[i]/(a[i]+b[i]*x[i]+c[i]*x[i]^2+d[i]*x[i]^3);
+
+s.t. budget: sum{i in I} y[i]*x[i] = 350;
+
+data;
+
+param:  l u a b c d :=
+1 10    60    56.49  1.67  -0.041  0.00030
+2 10    60    71.37  0.61  -0.016  0.00011
+3 15   120    23.88  2.05  -0.024  0.00009
+4 12.5 112.5  17.14  2.73  -0.035  0.00014
+5 15   135    72.38  0.34  -0.003  0.00001;
+ 
+option solver knitro; 
+option knitro_options "ms_enable=1";
+
+#option solver couenne; 
+
+solve;
+
+display f;
+print{i in 1..n} x[i];
+print{i in 1..n} y[i];

exercises/ex09/solutions/conv1i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c: x^2 + y^2 <= 1;
+
+option solver cplex;
+solve;

exercises/ex09/solutions/conv2i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c: x^2 + y^2 <= 1;
+
+option solver cplex;
+option cplex_options "reqconvex=2";
+solve;

exercises/ex09/solutions/conv3i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c: x + y <= 1;
+
+option solver cplex;
+option cplex_options "reqconvex=2";
+solve;
+display obj, x, y;

exercises/ex09/solutions/conv4i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c: x + y <= 1;
+
+option solver cplex;
+option cplex_options "reqconvex=3";
+solve;
+display obj, x, y;

exercises/ex09/solutions/conv5i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c: x + y <= 1;
+
+option solver gurobi;
+option gurobi_options "outlev=1";
+solve;
+display obj, x, y;

exercises/ex09/solutions/conv6i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c: x + y <= 1;
+
+option solver xpress;
+solve;
+display obj, x, y;;

exercises/ex09/solutions/conv7i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c: x + y <= 1;
+
+option solver scip;
+solve;
+display obj,x,y;

exercises/ex09/solutions/conv8i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c: x^2 + y^2 <= 1;
+
+option solver scip;
+solve;
+display obj, x, y;

exercises/ex09/solutions/conv9i.mod

+reset;
+
+var x integer, >= -2.5;
+var y integer, >= -2.5;
+minimize obj: x^2 - y^2;
+s.t. c1: x^2 + y^2 >= 1;
+s.t. c2: x^2 + y^2 <= 3;
+
+option solver scip;
+solve;
+display obj, x, y;