As far as I remember, in the context of optimization, "coordinate wise" means that you are manipulating each coordinate independently with the only criterion being that it improves your objective function. So you‘re zigzagging instead of taking a direct path. I can‘t remember where I read this, but in some cases, you can go through your coordinates in any order you want and still hit the optimum.
参考：
http://math.stackexchange.com/questions/28522/the-phrase-coordinate-wise-and-its-meaning
原文：http://www.cnblogs.com/xinping-study/p/4688145.html