## Section:
New Results2>
### Realistic step sizes
for optimization algorithms3>

Many theoretical results about objective improvement in the process of continuous optimization rely on the assumption that the steps of the algorithm are infinitesimally small, the only situation in which theoretical guarantees of improvement can be given. Y. Akimoto and Y. Ollivier have waived the necessity for such an assumption in a whole class of continuous optimization algorithms, thanks to the use of information geometry [20] . This takes theory closer to the practice of actual optimization algorithms.