Given two fixed vertices A and B on a plane, vertex A emits M rays and vertex B emits N rays, resulting in V intersection points. We can consider these V points as given.We select K points from the V intersection points, and no three points can be collinear.
Each selected point is denoted as the k-th intersection point, with distances d_1,k to A and d_2,k to B. The optimal K intersection points should satisfy the following objective:maximize log(1 + c1 * (d1,1 * d2,1)^(-2.5)) + log(1 + c2*(d_1,2 * d_2,2)^(-2.5)) + ... + log(1 + cK * (d1,K * d2,K)^(-2.5)),where the values of c_k are positive real constants.
The task is to determine how to choose the optimal K intersection points.I would like to obtain an algorithm that is as efficie.And I prefer to use more mathematical methods or algorithms rather than AI methods.nt as possible.
Since my current knowledge can only solve some simple non-convex problems, and I have not encountered this specific problem form nor do I know where to find the answer, I would greatly appreciate it if you could provide some directions or guidance on how to approach this problem.