Center-Points: A Link Between Discrete Geometry and Optimization

Optimality condition for mixed-integer convex minimization problems will be discussed and the concept of center-points, a generalization of the median from the one dimensional space to vector spaces. Through the theory of center-points, I will show how to extend the general cutting plane scheme from the continuous setting to the mixed-integer setting. Further, I will present several properties of center-points and how to compute them approximately.