# logistic regression without $L_2$-regularization does not have optimum?

I have a question related to machine learning. Consider the case when in the problem of binary classification the training set is linearly separable. How to show that in this case the optimization problem for logistic regression without $$L_2$$-regularization does not have optimum?

• Do you mean a unique optimum solution? Or an optimal objective value? – LinAlg Feb 10 at 15:12
• @LinAlg I mean a unique optimum solution. – Scout Feb 10 at 16:04
• That is exactly the concept of 'unique identification'. Look for 'identifiable' on the Wikipedia page of logistic regression. – LinAlg Feb 10 at 21:07