= Parameter continuity of variational regularization
For objectives $D+\alpha J$ with $J\ge0$ and positive parameter, suppose nearby-parameter <global minimizers> have uniformly bounded penalty, stay in a bounded set with <convergent subsequences>, and $D$ and $J$ are <sequentially lower semicontinuous> in the chosen <topology>. Their optimality inequalities and lower semicontinuity show that every subsequential limit minimizes the limiting objective. Uniqueness makes the regularized solution <continuous> in the parameter. Existence alone does not make an arbitrary selection among multiple <global minimizers> <continuous>.
Back to article page
