I'm trying to evaluate some classification algorithms' results in my imbalanced dataset. By imbalanced, I mean there are much more negative than positive labels. Accuracy and precision are always good, but recall, and Area Under the Precision-Recall curve (PR_AUC) are not so good. I'm seeking the classifier that maximizes the PR_AUC.

1.- Do you think this is a good criterion for selecting a classification algorithm?

2.- Are recall and PR_AUC proportional? I mean, if a classifier gives better recall results than another one but worse PR_AUC results... Am I doing something wrong? Or it has a logical explanation? Which one is the best criterion for imbalanced datasets?