From what I understand, the log barrier formulation is typically solved using Newton’s method. At least, the B&V textbook only mentions Newton’s method in this context. I wonder if this is because the log barrier can make the augmented objective severely ill-conditioned, causing first-order methods to struggle. While this may not be a major issue if feasibility is prioritized over optimality, I am still curious about how first-order methods might perform in practice in this setting.
Thanks for the insightful post.
From what I understand, the log barrier formulation is typically solved using Newton’s method. At least, the B&V textbook only mentions Newton’s method in this context. I wonder if this is because the log barrier can make the augmented objective severely ill-conditioned, causing first-order methods to struggle. While this may not be a major issue if feasibility is prioritized over optimality, I am still curious about how first-order methods might perform in practice in this setting.