Adjoint Methods in Computational Science, Engineering, and Finance (Dagstuhl Seminar 14371)

This report documents the program and the outcomes of Dagstuhl Seminar 14371 "Adjoint Methods in Computational Science, Engineering, and Finance". The development of adjoint numerical methods yields a large number of theoretical, algorithmic, and practical (implementation) challenges most of them to be addressed by state of the art Computer Science and Applied Mathematics methodology including parallel high-performance computing, domain-specific program analysis and compiler construction, combinatorial scientific computing, numerical linear algebra / analysis, and functional analysis. One aim of this seminar was to tackle these challenges by setting the stage for accelerated development and deployment of such methods based on in-depth discussions between computer scientists, mathematicians, and practitioners from various (potential) application areas. The number of relevant issues is vast, thus asking for a series of meetings of this type to be initiated by this seminar. It focused on fundamental theoretical issues arising in the context of "continuous vs. discrete adjoints." The relevant context was provided by presentations of various (potential) applications of adjoint methods in CSEF