mathematics

JuMP

JuMP is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand JuMP rather than just read about it. In short: JuMP is an algebraic modeling language and a collection of supporting packages for mathematical optimization embedded in the Julia programming language. JuMP is used by companies, government agencies, academic institutions, software projects, and individuals to formulate and submit optimization problems to third‑party solvers.

JuMP — illustration

Key takeaways

JuMP belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect JuMP to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of JuMP from memory before moving on to harder problems.

Reference excerpt

JuMP is an algebraic modeling language and a collection of supporting packages for mathematical optimization embedded in the Julia programming language. JuMP is used by companies, government agencies, academic institutions, software projects, and individuals to formulate and submit optimization problems to third‑party solvers. JuMP has been specifically applied to problems in the field of operations research.

Features JuMP is a Julia package and domain-specific language that provides an API and syntax for declaring and solving optimization problems. Specialized syntax for declaring decision variables, adding constraints, and setting objective functions is facilitated by Julia's syntactic macros and metaprogramming features. JuMP supports linear programming, mixed integer programming, semidefinite programming, conic optimization, nonlinear programming, and other classes of optimization problems. JuMP provides access to over 50 solvers, including state-of-the-art commercial and open-source solvers.

History JuMP was first developed by Miles Lubin, Iain Dunning, and Joey Huchette while they were students at the Massachusetts Institute of Technology. Today, JuMP's core developers are Miles Lubin, Benoît Legat, Joaquim Dias Garcia, Joey Huchette, and Oscar Dowson. Miles Lubin additionally holds the title of BDFL. JuMP is a sponsored project of NumFOCUS.

Recognition JuMP and its authors have been acknowledged by the 2015 COIN-OR Cup, the 2016 INFORMS Computing Society Prize, and the Mathematical Optimization Society's 2021 Beale – Orchard‑Hays Prize.

See also HiGHS optimization solver List of free and open-source optimization solvers Mathematical optimization PuLP – a similar project for Python Pyomo – Python packages for formulating optimization problems

References

External links JuMP documentation JuMP repository

Worked examples

Example 1 — a first encounter with JuMP

Start with the simplest possible case. Write down what JuMP claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to JuMP before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about JuMP ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of JuMP

In research: JuMP appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses JuMP in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: JuMP is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational science, Computer programming, Mathematical modeling, so understanding it makes those chapters shorter.
In everyday life: Look for JuMP outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study JuMP in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what JuMP means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain JuMP out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is JuMP in simple terms?

Why does JuMP matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study JuMP?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on JuMP.