From Duality Principle to Duality Technology
Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Duality plays a pivotal role in every field of science and engineering, but its concrete meaning is diverse. In search of duality-based technology duality concepts are classified and the role of duality in optimization and control is discussed. As fundamental duality phenomena in mathematics, emphasis is laid on the dual space in linear algebra and the Legendre transformation for convex functions. Duality between connotation and denotation is also explained. Two specific examples indicate recent fruitful interactions between different areas through duality.