Abstract: The research objective of this brief review paper is trying to introduce an optimization description for the classical (discrete) Minkowski problem to our mathematical readers, in the use of as plain and simple mathematical languages as possible. We also summarized some breakthroughs of the research history of classical Minkowski problem, and look forward to seeing a current breakthrough proposed. The classical Minkowski problem can be reduced to find solutions of the famous Monge-Ampere equation. The optimal transportation problem can be reduced to find solutions of the famous Monge-Ampere equation too. Optimal transport theory is an important application of the Minkowski problem. This brief review paper introduced the optimal transportation problem and its applications at the end of this paper. At present, the Monge–Kantorovich optimal transport has found applications in wide range in different fields (including image registration and warping, reflector design, retrieving information from shadowgraphy and proton radiography, seismic tomography and reflection seismology, etc.). In conclusion, the author of this brief review paper described and studied the classical Minkowski problem in optimization languages. Minkowski duality is also needed to study furthermore. This is an interesting research topic for optimization related researchers. There is a wealth of information and insight in the classical Minkowski problem and its optimal transportation problem. This studying is worth the effort.Abstract: The research objective of this brief review paper is trying to introduce an optimization description for the classical (discrete) Minkowski problem to our mathematical readers, in the use of as plain and simple mathematical languages as possible. We also summarized some breakthroughs of the research history of classical Minkowski problem, and look ...Show More
