ojAlgo is a pure Java numerical computing library providing high-performance linear algebra (dense and sparse matrices, decompositions like LU, QR, SVD, Cholesky, eigenvalue), optimization (linear programming via simplex, convex QP via active-set/ADMM, integer programming with branch-and-cut), neural networks, statistical distributions, random processes, time series analysis, clustering, financial portfolio models, and special functions. It has zero external dependencies and is modularized via JPMS. The architecture is a classic library: users create matrix objects or optimization models, invoke solvers or decompositions, and retrieve results. Key entry points include `MatrixStore`, `ExpressionsBasedModel`, `ArtificialNeuralNetwork`, and various decomposition factories. The codebase is well-tested with extensive unit and regression tests, and demonstrates strong engineering practices such as interface-driven design, factory patterns, and careful numerical stability. While primarily a software library, it also contains data analysis and research-oriented components (clustering, financial series, random processes), making it a hybrid but dominantly an application library.
MathOptInterface.jl is a Julia library providing a standardized abstraction layer for mathematical optimization. It defines a common interface for formulating optimization problems (variables, constraints, objectives) and communicating with solvers. The architecture is highly modular, with core types for functions and sets, a powerful bridge system that automatically transforms constraints into solver-supported forms, file format readers/writers (MPS, LP, NL, SDPA, CBF, MOF), and utilities for model management, copying, and automatic differentiation of nonlinear expressions. The package serves as the foundation for higher-level modeling systems like JuMP and is used by dozens of optimization solvers in Julia.
PySCIPOpt is a Python interface to the SCIP optimization solver, providing a comprehensive modeling environment for linear, mixed-integer, nonlinear, and constraint programming. The library wraps SCIP's C API through Cython, allowing users to formulate optimization problems using Python objects (variables, constraints, expressions) and to solve them with SCIP's state-of-the-art algorithms. The core architecture revolves around the `Model` class, which exposes all solver functionality, and a suite of plugin base classes (branching rules, heuristics, separators, constraint handlers, etc.) that enable users to customize the solution process. The expression system (`Expr`, `GenExpr`, `MatrixExpr`) supports algebraic formulation with operator overloading, while the recipes subpackage provides higher-level modeling helpers for common tasks such as piecewise linear constraints, infeasibility diagnosis, and convergence tracking. The repository is actively maintained and closely tracks SCIP releases, but also explicitly seeks new maintainers to sustain long-term development.
Uno is a modular C++ solver for nonlinearly constrained optimization (NLP, QP, LP). It implements a unification framework that combines interchangeable algorithmic ingredients—constraint relaxation strategies, inequality handling methods, Hessian models (exact, quasi-Newton, identity, zero), inertia correction, subproblem solvers (QP/LP), and globalization mechanisms (line search, trust region, filter, funnel). The solver supports both sequential quadratic programming (SQP) and interior-point methods, and can be configured via presets that mimic established solvers like filterSQP and IPOPT. The architecture is a library with a main orchestration loop in `Uno.cpp`. The user defines the optimization problem through callback functions (objective, gradient, Jacobian, Hessian) via a C API, which is then wrapped by interfaces for AMPL, Fortran, Julia, and Python. Internally, the solver builds a regularized KKT system, delegates subproblem solves to external libraries (HiGHS, BQPD, HSL MA27/57/86, MUMPS, SPRAL), and applies globalization to ensure convergence. The codebase is heavily templated and uses expression templates for linear algebra, factory patterns for component selection, and runtime dynamic loading for optional dependencies. Key entry points include `uno_optimize()` (C API), `UnoSolverWrapper::optimize()` (Python), and the AMPL executable `uno_ampl`. The solver is used in research and production environments via JuMP.jl, CasADi, pyOptSparse, and OpenMDAO. External dependencies include BLAS/LAPACK, HSL (proprietary), MUMPS, SPRAL, HiGHS, BQPD, and AMPL ASL. The project is actively maintained with extensive CI, cross-platform builds, and a growing ecosystem of language bindings.