CSC 2411 - Linear Programming and Combinatorial Optimization ∗ Lecture 8 : Interior Point Method and Semi Definite Programming

In the last lecture, we were introduced to the Interior Point Method. The simplex method solves linear programming problems (LP) by visiting extreme points (vertices) on the boundary of the feasible set. In contrast, the interior point method is based on algorithms that find an optimal solution while moving in the interior of the feasible set. Intuitively, in each iteration of the interior point method we improve a combination of the objective function while trying to stay away from the boundary. Since we know that the solution to an LP lies on the boundary of the polytope, once the value of the objective function is close to its optimum we find the closest vertex and declare it as the optimum solution. Below we briefly review some definitions and then we will discuss how the Ye’s Interior Point Method moves in the interior of the polytope to find the optimal vertex.