Optimal step length for the Newton method: case of self-concordant functions

The theoretical foundation of path-following methods is the performance analysis (damped) Newton step on class self-concordant functions. However, bounds available in literature and used design are not optimal. In this contribution we use optimal control theory to compute length method functions, as a function initial decrement, resulting worst-case decrease decrement. exact expressed terms solutions ordinary differential equations which cannot be integrated explicitly. We provide approximate numerical analytic expressions accurate enough for optimization methods. Consequently, neighbourhood central path iterates required stay can enlarged, enabling faster progress along during each iteration hence fewer iterations achieve given accuracy.