Advances to modeling and solving infinite-dimensional optimization problems in InfiniteOpt.jl

Abstract

This paper details two extensions for the unifying abstraction behind InfiniteOpt.jl: infinite-dimensional generalized disjunctive programming (InfiniteGDP) and GPU-compatible direct transcription solution techniques with an abstraction called InfiniteSIMD-NLP. InfiniteOpt.jl is a Julia package that provides an efficient framework for formulating and solving a wide range of infinite-dimensional optimization (InfiniteOpt) problems. The InfiniteGDP abstraction builds upon traditional GDP techniques to enable intuitive modeling of discrete events and complex logic over continuous domains (e.g., position, time, and/or uncertainty); this abstraction is implemented in InfiniteDisjunctiveProgramming.jl. Moreover, the InfiniteSIMD-NLP abstraction, implemented in InfiniteExaModels.jl, exploits the recurrent structure of transcribed InfiniteOpt problems to efficiently discretize, differentiate, and solve such problems on high performance CPU and GPU architectures. We use a diverse set of case studies in dynamic, PDE-constrained, and stochastic optimization to demonstrate the relative merits of these abstraction extensions. The results demonstrate the utility of the InfiniteGDP abstraction to model continuous space–time switching constraints and how the InfiniteSIMD-NLP abstraction is able to accelerate the solution of InfiniteOpt problems by one to two orders-of-magnitude relative to existing state-of-the-art approaches.