I'm studying the lecture on the Machine Learning at Coursera.
When introducing the cost function for Logistic Regression, they said that we shouldn't use the same cost function as the one for Linear Regression since that cost function can have multiple local minima that would cause gradient descent to fail.
However, I'm having a hard time finding an example of an equation which would result in multiple local minima if one uses the Linear Regression cost function on Logistic Regression.
Could someone please provide such an example and give me some intuition about why it occurs?
Side note: I can see other good properties of using the log(h(x)) cost function for logistic regression, that it strongly penalizes being certain when you're actually wrong. But I'm trying to understand the claim that the linear regression's cost function will be non-convex for logistic regression.