Gradient descent multidimensional linear regression - does learning rate affects concurrency?
If you use a convex loss function you always have one optimum point, and you will always be able to find it. 


  I have done some calculations and I get correct results but not for all learning rates I tried to specify.


The reason is that you may have selected a large learning rate which may lead to overshoot the optimum. It also may be so small that you don't reach to the desired point and it all depends on your data. If you use the simple gradient descent algorithm, it is an incident that can be seen a lot. You can use other optimisation techniques like Adam which is much more better and you rarely see these problems.