InfiniteOpt.jl is a JuMP extension for expressing and solving infinite-dimensional optimization problems. Such areas include stochastic programming, dynamic programming, space-time optimization, and more. InfiniteOpt serves as an easy-to-use modeling interface for these advanced problem types that can be used by those with little background in these areas. It also it contains a wealth of capabilities making it a powerful and convenient tool for advanced users.

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InfiniteOpt builds upon JuMP to add support for many complex modeling objects which include:

  • Infinite parameters (for example, time, space, and/or uncertainty)
  • Finite parameters (similar to ParameterJuMP)
  • Infinite variables (decision functions) (for example, $y(t, x)$)
  • Derivatives (for example, $\frac{\partial y(t, x)}{\partial t}$)
  • Measures (for example, $\int_{t \in T}y(t, x)dt$ and $\mathbb{E}[y(\xi)]$)
  • First class nonlinear modeling

The unifying modeling abstraction behind InfiniteOpt captures a wide spectrum of disciplines which include dynamic, PDE, stochastic, and semi-infinite optimization. Moreover, we facilitate transferring techniques between these to synthesize new optimization paradigms.


InfiniteOpt is licensed under the MIT "Expat" license.


InfiniteOpt.jl is a registered Julia package and can be installed by entering the following in the REPL.

julia> import Pkg; Pkg.add("InfiniteOpt")


Please visit our documentation pages to learn more. These pages are quite extensive and feature overviews, guides, manuals, tutorials, examples, and more.


For additional help please visit and post in our discussion forum.



If you use InfiniteOpt.jl in your research, we would greatly appreciate your citing it.

      title = {A unifying modeling abstraction for infinite-dimensional optimization},
      journal = {Computers & Chemical Engineering},
      volume = {156},
      year = {2022},
      issn = {0098-1354},
      doi = {https://doi.org/10.1016/j.compchemeng.2021.107567},
      url = {https://www.sciencedirect.com/science/article/pii/S0098135421003458},
      author = {Joshua L. Pulsipher and Weiqi Zhang and Tyler J. Hongisto and Victor M. Zavala},

A pre-print version is freely available though arXiv.