JuMP is a modeling interface and a collection of supporting packages for mathematical optimization that is embedded in Julia. With JuMP, users formulate various classes of optimization problems with easy-to-read code, and then solve these problems using state-of-the-art open-source and commercial solvers. JuMP also makes advanced optimization techniques easily accessible from a high-level language.
JuMP will be participating as a sub-organization in NumFOCUS's application for Google Summer of Code 2021. For more information about this application see:
If you have an idea for GSOC2021, please make a pull request to edit this page.
A key limitation of the current version of JuMP and MathOptInterface is that they are limited to problems with a single scalar objective function. The goal of this project is to relax this requirement so that users can model and solve multi-objective optimization problems.
| Priority | Involves | Mentors |
|---|---|---|
| Medium | Adding support for vector-valued objective functions to MOI and JuMP | Oscar Dowson |
Technical details available in this issue
- Knowledge of JuMP and MathOptInterface
- Knowledge of multi-objective optimization
Initial steps
- Read Issue 2099
- Become familiar with previous attempts at vector-valued objectives in JuMP https://github.com/anriseth/MultiJuMP.jl
Key deliverables
- Add tests, documentation, and features for vector-valued objective problems to MathOptInterface.
- Here was the start of a previous attempt: jump-dev/MathOptInterface.jl#968.
- Also a reader for the MOP file format: odow/MathOptFormat.jl#95
- Revive this solver for proof-of-concept: https://github.com/odow/MOO.jl.
- Add more tests, documentation, and features.
- Add other multi-objective algorithms
Stretch goal
- Extend JuMP's
@objectivemacro to work with vector-valued functions. - Add support for vOptSolver
| Priority | Involves | Mentors |
|---|---|---|
| Medium | Implementation of problem matrix representations and integration in solvers | Joaquim Dias Garcia, Mathieu Besançon, Benoît Legat |
Many classes of optimization problems are commonly represented using matrices of parameters:
l ≤ A x ≤ u
These representations can be what optimization solvers require as input or used to transform optimization problems, for example to derive its dual problem or its KKT conditions. We want to develop MatrixOptInterface.jl to federate efforts to build various representations of optimization problems in matrix form.
The core of the project will the implementation of matrix representations for optimization problems. These representations can then be used to simplify the code in solver wrappers transforming a MathOptInterface model into structures that are passed to the native solver.
Beyond the implementation of the various matrix forms, this project will lead possibilities to work on various connected packages such as solver wrappers, Dualization.jl, DiffOpt.jl, or ParametricOptInterface.jl.
- Knowledge of mathematical optimization (linear, quadratic optimization, duality)
- Basic knowledge of MathOptInterface
Initial steps
- Read the MathOptInterface manual and get familiar with the data structures used to represent scalar and vector functions
- Read on the models already implemented in matrix form
Key deliverables
- Implement various forms for linear, conic and quadratic optimization problems in MatrixOptInterface
- Design user-oriented documentation for building and consuming the various problem formats
- Replace the conversion code from MOI structures in solvers with the MatrixOptInterface implementation
Stretch goals
- Integrate MatrixOptInterface in ParametricOptInterface, Dualization.jl, DiffOpt.jl, BilevelJuMP.jl
Chordal decomposition is a key step in the formulation of sparse SDP. Implementations are already available in SumOfSquares and COSMO.
| Priority | Involves | Mentors |
|---|---|---|
| Medium | Creating Chordal extension and decomposition packages | Joaquim Dias Garcia, Benoît Legat, Theo Diamandis |
Many semidefinite problems are sparse and exploiting this sparsity can significantly reduce the computation time and memory needed to solve the problem.
The goal of this project is to refactor existing implementation of chordal sparsity reduction into a MathOptInterface layer that is easy to plug into any SDP solver as a transformation layer.
Chordal decomposition and PSD matrix completion for SDPs are not currently accessible through MathOptInterface. The core goal of this project is to create an MOI layer for chordal decomposition and allow these capabilities to be easy options from JuMP that work with any SDP solver. Then, this package will be used to create sparse SDP examples for JuMP, drawing from several application areas. Finally, there is the possibility of working on improvements to chordal graph algorithms themselves.
- Knowledge of mathematical optimization (semidefinite programming)
- Knowledge of graph theory and chordal graphs (see Chordal Graphs and Semidefinite Optimization by Lieven Vandenberghe and Martin S. Andersen)
- Basic knowledge of MathOptInterface
Initial steps
- Read the MathOptInterface manual and get familiar with the data structures used to represent scalar and vector functions
- Read Chordal Graphs and Semidefinite Optimization by Lieven Vandenberghe and Martin S. Andersen and A Clique Graph Based Merging Strategy for Decomposable SDPs by Michael Garstka, Mark Cannon, and Paul Goulart to familiarize yourself with the use of chordal sparsity in semidefinite programming
- Read the implementation of algorithms on chordal graphs in SumOfSquares, COSMO, and ChordalDecomp.jl
Key deliverables
- Create a ChordalOptInterface.jl package an MOI layer doing chordal sparsity decomposition
- Allow chordal decomposition to be an easy to use option from JuMP that works with any semidefinite solver
- Add examples that use chordal decomposition to solve large-scale sparse semidefinite programs in applications of interest
Stretch goals
- Improve algorithms for chordal decomposition in the currently-under-development ChordalDecomp.jl