The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as Python and MATLAB. This paper explores how Julia, a modern programming language for numerical computing which claims to bridge this divide by incorporating recent advances in language and compiler design (such as just-in-time compilation), can be used for implementing software and algorithms fundamental to the field of operations research, with a focus on mathematical optimization. In particular, we demonstrate algebraic modeling for linear and nonlinear optimization and a partial implementation of a practical simplex code. Extensive cross-language benchmarks suggest that Julia is capable of obtaining state-of-the-art performance.
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> Imagine if you did dev on Julia - how do you hire devs?
Julia doesn't take long to learn if you've ever written any Python, or Matlab, or R. It's very good at calling into existing code written in other languages (the above, and C) so it's possible to transition gradually.
> I'm also curious to know 'how much faster' it is - couldn't those performance problems be solved with more horsepower?
Depends on the exact type of computation. If everything you're doing is straight BLAS/LAPACK or other library calls, then Python is just glue code and not taking much of the time. If you're implementing your own custom algorithms (or writing libraries) that are difficult to express…
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in a vectorized way (where numpy just does the work in C) or you want more customized data structures and types than dense arrays of single or double precision floating point numbers, Julia will do well. There are various projects out there that try to make Python faster (PyPy, Numba, Pyston, Pyjion, the list seems to grow every few months) but it's a very difficult problem to do in full generality since you either have to restrict yourself to a subset of the language where the semantics permit optimizations, or lose compatibility with all the C-extension libraries you're used to. Julia has designed the language semantics and the conventions of the standard library to be more amenable to optimization. It's early days yet in terms of multithreading support, but Julia has a better story there as well.
For a representative performance comparison case study, see section 4 of https://arxiv.org/pdf/1312.1431v1.pdf. There have been similar experiences reported and published in other application areas since.
If you're interested in model generation time, have a look at JuMP (https://github.com/JuliaOpt/JuMP.jl). More discussions on the speed of modeling languages at http://arxiv.org/abs/1312.1431 and http://arxiv.org/abs/1508.01982
The language I used, JuMP [1], is quite similar to AMPL. In fact in [2] we do performance comparisons with it. Check it out if you have a chance.
[1] https://github.com/JuliaOpt/JuMP.jl
[2] http://arxiv.org/abs/1312.1431
Very cool. We had a similar experience when implementing the Simplex method for linear optimization, except we evaluated PyPy versus Julia instead of Cython. Its similar in that it benchmarks "just" the language, not BLAS, which is common pitfall I see when people compare the two. I guess at this point, a year or so later, it isn't surprising to me anymore that Julia is as fast as it is for these sorts of computational tasks - its been demonstrated pretty comprehensively at this point.
Slides: http://www.mit.edu/~mlubin/informs2013.pdf
Paper: http://arxiv.org/abs/1312.1431
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.
Artificial intelligence (AI) researchers have been developing and refining large language models (LLMs) that exhibit remarkable capabilities across a variety of domains and tasks, challenging our understanding of learning and cognition.