The field of inverse problems has existed in many branches of earth sciences, physical sciences, engineering and mathematics for a long time. Inverse problems are typically ill-posed. In recent years, different inverse problems in frontiers of sciences appear. Standard methods for inverse problems are regularization methods. In addition, optimization methods are widely used in other science and engineering fields, for example, big data and intelligent computing, geophysical prospecting, transportation, biology, communication and image processing. Meanwhile, optimization methods have also been applied in computational inversion applications.
