A unifying modeling abstraction for infinite-dimensional optimization

Infinite-dimensional optimization (InfiniteOpt) problems involve modeling components (variables, objectives, and constraints) that are functions defined over infinite-dimensional domains. Examples include continuous-time dynamic (time is an infinite domain a function of time), PDE (space time domains space-time), as well stochastic semi-infinite (random space such random space). InfiniteOpt also arise from combinations these problem classes (e.g., optimization). Given the nature objectives constraints, one often needs to define appropriate quantities (measures) properly pose problem. Moreover, need be transformed into finite dimensional representation so they can solved numerically. In this work, we present unifying abstraction facilitates modeling, analysis, solution problems. The proposed enables general treatment provides measure-centric paradigm handle associated variables, constraints. This allows us transfer techniques across disciplines with identify new, interesting, useful paradigms event constraints risk measures domains). Our serves backbone intuitive Julia-based package call InfiniteOpt.jl. We demonstrate developments using diverse case studies arising in engineering.