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A JuMP
extension for expressing and solving infinite-dimensional optimization
problems.
!!! note
InfiniteOpt v0.6
introduces JuMP
's new general nonlinear modeling to InfiniteOpt
!
Please see [Nonlinear Expressions](@ref nlp_guide) for more information.
InfiniteOpt.jl
provides a general mathematical abstraction to express and solve
infinite-dimensional optimization problems (i.e., problems with decision
functions). Such problems stem from areas such as space-time programming and
stochastic programming. InfiniteOpt
is meant to facilitate intuitive model
definition, automatic transcription into solvable models, permit a wide range
of user-defined extensions/behavior, and more.
It builds upon JuMP
to add support for many complex modeling objects which
include:
- Infinite parameters (e.g., time, space, uncertainty, etc.)
- Finite parameters (similar to
ParameterJuMP
) - Infinite variables (e.g.,
y(t, x)
) - Derivatives (e.g.,
\frac{\partial y(t, x)}{\partial t}
) - Measures (e.g.,
\int_{t \in \mathcal{D}_t}y(t,x) dt
,\mathbb{E}[y(\xi)]
) - More
!!! note
InfiniteOpt
is intended to be used for infinite-dimensional optimization
problems. Finite problems (e.g., directly modeling a discrete time model)
should instead be modeled using JuMP
.
Moreover, InfiniteOpt
decouples the infinite-dimensional formulations from the
finite transformations typically used to solve them. This readily enables diverse
techniques be used to solve these types of problems. By default, we employ
direct transcription (i.e., discretization) transformations whose features
include:
- Efficient implementations that scale linearly!
- Diverse integral approximations (e.g., quadratures, sampling)
- Diverse derivative approximations (e.g., finite difference, orthogonal collocation)
- Sophisticated support point management system
- Compatible with all JuMP-supported solvers
Accepted infinite/finite problem forms currently include:
- Variables
- Continuous and semi-continuous
- Binary
- Integer and semi-integer
- Semi-definite
- Derivatives
- Ordinary derivative operators (of any order)
- Partial derivative operators (of any order)
- Measures
- Univariate and multivariate integrals
- Univariate and multivariate expectations
- Arbitrary measure operators (via general measure API)
- Objectives
- Linear
- Quadratic (convex and non-convex)
- General nonlinear
- Constraints
- Linear
- Quadratic (convex and non-convex)
- General nonlinear
- Conic
- Semi-definite
- Indicator
See our YouTube overview of infinite-dimensional programming and InfiniteOpt.jl's capabilities from JuliaCon 2021 (note that nonlinear support has since been added):
InfiniteOpt.jl
is a registered Julia
package and can be added simply by
inputting the following in the package manager:
(v1.9) pkg> add InfiniteOpt
Please visit our Installation Guide for more details and information on how to get started.
InfiniteOpt
is extension of JuMP
, thus new users should start by
familiarizing themselves with how to use JuMP
first. See
JuMP
's documentation to learn more.
Once you're familiar with JuMP
check out our Quick Start Guide to get
started. From there we provide extensive documentation to help you along, please
see How to Use the Documentation for more info.
InfiniteOpt
is intended to serve both as a high-level interface for
infinite-dimensional optimization and as a highly customizable/extendable
platform for implementing advanced techniques. With this in mind, we provide the
User Guide
sections to walk through the ins and outs of InfiniteOpt
. Each
page in the User Guide
typically contains the following:
- An
Overview
section describing the purpose of the page. - A
Basic Usage
section to guide usingInfiniteOpt
at a high level. - Other sections offering more in-depth information/guidance beyond basic usage.
We also provide a technical manual in the API Manual
sections which are
comprised of the docstrings of all the public methods and types that comprise
InfiniteOpt
. These detail the technical aspects of each function, method, macro,
and composite type.
Details, instructions, templates, and tutorials on how to write user-defined
extensions in InfiniteOpt
are provided on the Extensions page.
Finally, case study examples are provided in the Examples
sections.
For additional help please visit and post in our Discussion Forum.
InfiniteOpt
is a powerful tool with a broad scope lending to a large realm of
possible feature additions and enhancements. So, we are thrilled to support
anyone who would like to contribute to this project in any way big or small.
For small documentation fixes (such as typos or wording clarifications) please do the following:
- Click on
Edit on GitHub
at the top of the documentation page - Make the desired changes
- Submit a pull request
For other contributions, please visit our [Developers Guide](@ref contribute_guide) for step-by-step instructions and to review our style guide.
If you use InfiniteOpt.jl in your research, we would greatly appreciate your citing it.
@article{pulsipher2022unifying,
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.
We acknowledge our support from the Department of Energy under grant DE-SC0014114.