[Convex Optimization] Interior-Point Method with Barrier Function

• Optimization algorithm commonly used to solve convex optimization problems using Newton method
• starts with perturbed KKT by introducing a perturbation variable to complementary slackness condition
• involves introducing a barrier function into the objective function to create a modified problem that is easier to solve.
  • barrier function acts as a barrier that prevents the algorithm from reaching points outside of the feasible region. (inequality boundary)
  • typically a logarithmic function that approaches infinity as the solution approaches the equality boundary
• solves equality constrained optimization problem by iteratively improving the solution untill the improvement is below certain threshold

Summary Notes

• Interior-Point Method with Barrier