I am dealing with an optimization problem that has a large number of variables to optimize over - for example let's call these variables $x$, $y$, and $z$ and I wish to minimize the function $f(x,y,z)$. The optimization method that I am using is not able to handle optimizing over all the variables at once. I am instead simplifying the problem by optimizing over a single variable at a time while keeping the other variables fixed. I.e. I fix $y=y_0$, and $z=z_0$ and then optimize the function only over $x$. This 1D optimization yields some optimal value $x^*$. I then fix $x=x^*$, $z=z_0$, then optimize over $y$. I realize that this doesn't necessarily provide me with a globally optimal solution but it should yield a local minimum. I am wondering what the name of this method is and where I can find any information about it. Also if there is a more appropriate community to ask, please let me know. ThanksEdit: the optimization is conducted over $x$, then $y$, then $z$, then $x$, and so on until the solution converges.
Name of an Optimization Approach to Reduce Size of Variable Space
optimization;terminology
This is coordinate descent. I believe it's used on very large-scale problems when other methods like gradient descent might be too slow (e.g., http://epubs.siam.org/doi/abs/10.1137/100802001). It should converge to a local minimum, but it also would require more steps than something like gradient descent or Newton-type methods.