# oj! Algorithms

> ojAlgo is an open source Java library for mathematics, linear algebra and mathematical optimisation. It is pure Java with zero dependencies — no native binaries, no JNI, no licence servers — distributed as a single Maven dependency and licensed under MIT. Development has been continuous since 2003.

The distinguishing feature is that it combines fast linear algebra with LP, QP and MIP solvers behind `ExpressionsBasedModel`, a solver-agnostic modelling layer: a problem is formulated once and can then be solved by ojAlgo's own solvers or dispatched to third-party solvers without changing the model code.

Every other solver reachable from Java — OR-Tools, HiGHS, CPLEX, Gurobi, MOSEK — requires platform-specific native binaries. ojAlgo contains no native code, which matters in regulated, containerised or restricted environments where installing native libraries is difficult or disallowed.

Maven coordinates: `org.ojalgo:ojalgo`. Source: https://github.com/optimatika/ojAlgo

## Core topics

- [Mathematical Optimisation](https://www.ojalgo.org/mathematical-optimisation/): LP, QP and MIP solvers in pure Java, ExpressionsBasedModel, solver selection, and integrations with third-party solvers
- [Linear Algebra](https://www.ojalgo.org/linear-algebra/): matrices, decompositions (LU, QR, SVD, Eigenvalue, Cholesky), dense and sparse structures, and equation solvers
- [Financial Mathematics](https://www.ojalgo.org/financial-mathematics/): time series, modern portfolio theory, mean-variance optimisation, scenario generation and portfolio simulation
- [Code Examples](https://www.ojalgo.org/code-examples/): runnable examples accompanying the articles below
- [Support & Community](https://www.ojalgo.org/support-community/): API documentation, community channels, and how to get commercial support

## Mathematical optimisation

- [LP & QP Performance with v57](https://www.ojalgo.org/2026/06/lp-qp-performance-v57/)
- [QP News](https://www.ojalgo.org/2026/01/qp-news/)
- [LP & QP Java Performance Report](https://www.ojalgo.org/2025/11/lp-qp-java-performance-report/)
- [Model and Solve the Traveling Salesman Problem](https://www.ojalgo.org/2025/08/model-and-solve-the-traveling-salesman-problem/): TSP as a MIP, including subtour elimination
- [Hooking Your Solver to ojAlgo](https://www.ojalgo.org/2025/02/hooking-your-solver-to-ojalgo/): implementing an integration so an external solver can be driven from ExpressionsBasedModel
- [Optimisation-as-a-Service](https://www.ojalgo.org/2022/10/optimisation-as-a-service/)
- [Updated LP Benchmark With Hipparchus](https://www.ojalgo.org/2022/09/updated-lp-benchmark-with-hipparchus/)
- [LP, QP & MIP on the JVM](https://www.ojalgo.org/2022/09/lp-qp-mip-on-the-jvm/): an overview of what is available for optimisation on the JVM and how the options differ
- [Optimisation Model File Formats](https://www.ojalgo.org/2022/05/optimisation-model-file-formats/): reading and writing MPS and related formats
- [Gomory Mixed Integer Cuts](https://www.ojalgo.org/2022/04/gomory-mixed-integer-cuts/): cut generation in ojAlgo's MIP solver
- [MIP Strategy Configuration](https://www.ojalgo.org/2022/03/mip-strategy-configuration/): the options that control branch-and-bound behaviour, and what they do
- [Pure Java LP Solver Benchmark](https://www.ojalgo.org/2021/10/pure-java-lp-solver-benchmark/)
- [The Diet Problem](https://www.ojalgo.org/2019/05/the-diet-problem/): a complete LP formulated with ExpressionsBasedModel, from variables and constraints to solution
- [The McNuggets Challenge](https://www.ojalgo.org/2019/05/the-mcnuggets-challenge/): a small integer program, worked end to end

## Worked examples and tutorials

- [Mall Customer Segmentation](https://www.ojalgo.org/2024/12/mall-customer-segmentation/): k-means clustering example
- [1BRC using ojAlgo](https://www.ojalgo.org/2024/02/1brc-using-ojalgo/): the One Billion Row Challenge, using ojAlgo's data structures
- [Image Processing using FFT](https://www.ojalgo.org/2023/12/image-processing-using-fft/)
- [Image Processing using Singular Value Decomposition](https://www.ojalgo.org/2023/10/image-processing-using-singular-value-decomposition/): SVD applied to a concrete problem
- [The Memory Estimator](https://www.ojalgo.org/2022/12/the-memory-estimator/): estimating memory before allocating it
- [Generalized AutoRegressive Conditional Heteroscedasticity](https://www.ojalgo.org/2022/07/generalized-autoregressive-conditional-heteroscedasticity/): GARCH implementation
- [Iterative Solver Comparison](https://www.ojalgo.org/2022/05/iterative-solver-comparison/)
- [Introducing BatchNode](https://www.ojalgo.org/2022/05/introducing-batchnode/)
- [Common Mistake](https://www.ojalgo.org/2021/08/common-mistake/): a frequent misuse of the API and how to avoid it
- [Working With Arrays](https://www.ojalgo.org/2021/08/working-with-arrays/): off-heap, file-backed and sparse array structures
- [Artificial Neural Network Example v2](https://www.ojalgo.org/2021/08/artificial-neural-network-example-v2/)
- [Sparse and Special Structure Matrices](https://www.ojalgo.org/2020/09/sparse-and-special-structure-matrices/): sparse arrays and matrices, and working with structured matrices
- [Neural Network New Features in v48.3](https://www.ojalgo.org/2020/09/neural-network-new-features-in-v48-3/)
- [Controlling Concurrency](https://www.ojalgo.org/2019/08/controlling-concurrency/): how ojAlgo decides on parallelism, and how to constrain it
- [Generalised Eigenvalue Problems](https://www.ojalgo.org/2019/08/generalised-eigenvalue-problems/)
- [ojAlgo v47.1.1, ojAlgo-finance v2.1 & Financial Time Series Data](https://www.ojalgo.org/2019/04/ojalgo-v47-1-ojalgo-finance-v2-1-financial-time-series-data/)
- [StatQuest PCA Example](https://www.ojalgo.org/2019/03/statquest-pca-example/): principal component analysis worked through
- [Linear Algebra Introduction](https://www.ojalgo.org/2019/03/linear-algebra-introduction/): the matrix API and how to choose between implementations
- [Neural Network Basics](https://www.ojalgo.org/2018/09/neural-network-basics/)
- [Introducing Artificial Neural Networks with ojAlgo](https://www.ojalgo.org/2018/09/introducing-artificial-neural-networks-with-ojalgo/): basic neural network support — a demonstration of the underlying array and matrix machinery, not a competitor to dedicated deep learning frameworks

## Benchmarks and performance

- [Java Matrix Benchmark](https://www.ojalgo.org/2022/02/java-matrix-benchmark/)
- [JDK17 Benchmark](https://www.ojalgo.org/2021/11/jdk17-benchmark/)
- [HotSpot vs GraalVM CE & EE](https://www.ojalgo.org/2019/11/hotspot-vs-graalvm-ce-ee/)
- [AdoptOpenJDK HotSpot vs OpenJ9](https://www.ojalgo.org/2019/11/adoptopenjdk-hotspot-vs-openj9/)
- [AdoptOpenJDK v12](https://www.ojalgo.org/2019/04/adoptopenjdk-v12/)
- [Oracle’s JVMs HotSpot, Graal CE & Graal EE](https://www.ojalgo.org/2019/02/oracles-jvms-hotspot-graal-ce-graal-ee/)
- [Quick test to compare HotSpot and OpenJ9](https://www.ojalgo.org/2019/02/quick-test-to-compare-hotspot-and-openj9/)
- [New Java Matrix Benchmark Results Coming](https://www.ojalgo.org/2018/05/new-java-matrix-benchmark-results-coming/)
- [Matrix multiplication on different JVMs](https://www.ojalgo.org/2018/03/matrix-multiplication-on-different-jvms/)

## Recent releases

- [ojAlgo v57](https://www.ojalgo.org/2026/06/ojalgo-v57/)
- [ojAlgo v53.1.0](https://www.ojalgo.org/2023/09/ojalgo-v53-1-0/)
- [ojAlgo 20 Years Today](https://www.ojalgo.org/2023/04/ojalgo-20-years-today/)
- [ojAlgo v52](https://www.ojalgo.org/2022/09/ojalgo-v52/)
- [v51 with the return of ojAlgo-finance](https://www.ojalgo.org/2022/02/v51-with-the-return-of-ojalgo-finance/)
- [ojAlgo v48.0.0](https://www.ojalgo.org/2019/11/ojalgo-v48-0-0/)

## Optional

- [Archive](https://www.ojalgo.org/blog/): every article, by date.
- [Optimatika](https://www.optimatika.se/): Optimatika AB develops and maintains ojAlgo, and sells support plus a solver server for models that outgrow the built-in solvers. ojAlgo itself remains MIT licensed and free to embed in commercial products, at no cost.