SVM algorithms have basically advantages in terms of complexity. First I would like to clear that both Logistic regression as well as SVM can form non linear decision surfaces and can be coupled with the kernel trick. If Logistic regression can be coupled with kernel then why use SVM?

● SVM is found to have better performance practically in most cases.

● SVM is computationally cheaper O(N^2*K) where K is no of support vectors (support vectors are those points that lie on the class margin) where as logistic regression is O(N^3)

● Classifier in SVM depends only on a subset of points . Since we need to maximize distance between closest points of two classes (aka margin) we need to care about only a subset of points unlike logistic regression.