How different is the cost function optimization in SVM and neural network

Question

SVM and neural networks are very popular machine learing techniques. But I read that the optimization functions of one is convex and for the other is non-convex.

How does neural network involve optimizing non-convex functions and a SVM involve convex optimization?

Answer 1

Not sure I fully understood your problem, but regarding SVM and its view as convex optimization problem - you could read this short paper: http://www.cs.cmu.edu/~epxing/Class/10701-08s/recitation/svm.pdf

Why ANNs cost function is non-convex is answered here (especially good answer from mr. Roland): https://stats.stackexchange.com/questions/106334/cost-function-of-neural-network-is-non-convex