I am new to PROLOG, but have a problem that I wish to solve. I am trying to design a layout manager for a domino game application. Below is a sampling of what I am trying to do. Can anyone provide me with a simple example of optimization using CLP(R) with the CIAO system or answer the example below?

Take two angles A1 and A2 with a domain -45 to 45. Let X1 = 10*cos(A1)+5 Let Y1 = 3+10*sin(A1) Let X2 = 6*sin(A1)+5 Let Y2 = 3-5*cos(A1) Let X3 = 10*cos(A2)+5 Let Y3 = 3+10*sin(A2) Let X4 = 6*sin(A2)+5 Let Y4 = 3-5*cos(A1)

Satisfy ((X3-X4)*(X1-X3)+(Y3-Y4)*(Y1-Y4))>0 AND ((X3-X4)*(X2-X3)+(Y3-Y4)*(Y2-Y4))>0 constraint (a constraint of dot products of vectors) Use an objective function minimize the sum of A1+A2.