I found the answers above helpful, but still a little confusing. Here's what ultimately worked for me. There are 2 views involved in this example, a parent Constraint View and a child of the Constraint View.
// Get the constraint layout of the parent constraint view.
ConstraintLayout mConstraintLayout = findViewById(R.id.parentView);
// Define a constraint set that will be used to modify the constraint layout parameters of the child.
ConstraintSet mConstraintSet = new ConstraintSet();
// Start with a copy the original constraints.
mConstraintSet.clone(mConstraintLayout);
// Define new constraints for the child (or multiple children as the case may be).
mConstraintSet.constrainPercentWidth(R.id.childView, 0.5F);
mConstraintSet.constrainPercentHeight(R.id.childView, 0.7F);
// Apply the constraints for the child view to the parent layout.
mConstraintSet.applyTo(mConstraintLayout);
Note that for some reason, a percentage constraint of 1.0F doesn't work, although 0.99F works just fine.