👉 Interior Point Method (IPM), also known as the Barrier Method, is an optimization technique used to solve linear and convex quadratic programming problems. Unlike traditional methods like the Simplex algorithm, which traverse the vertices of the feasible region, IPM uses barrier functions to guide the search within the interior of the feasible set. This approach avoids the need for explicit feasibility checks at each step, making it more efficient for large-scale problems with many constraints. IPM transforms the original constrained optimization problem into a series of unconstrained problems by introducing a barrier function that penalizes solutions as they approach the boundary of the feasible region. As the method progresses, this barrier function becomes increasingly steep, ensuring that the solution remains strictly within the interior until the optimal point is reached. This makes IPM particularly effective for problems where the feasible region is complex or has a large number of constraints.
