CPLEX

CPLEX is a high-performance mathematical optimization solver developed by IBM. It is designed to solve linear programming (LP), mixed-integer programming (MILP), quadratic programming (QP), quadratically constrained programming (QCP), and related optimization problems. CPLEX is widely used in operations research, supply chain, finance, and scheduling to obtain optimal or near-optimal solutions for large-scale models.

The solver provides multiple modeling interfaces. The Concert technology offers APIs for C++, Java, and .NET to build optimization models, while the Optimization Programming Language (OPL) provides a declarative modeling option used with IBM CPLEX Optimization Studio. In addition, CPLEX can be accessed from Python, MATLAB, and R, and runs on Windows, Linux, and macOS.

CPLEX employs specialized algorithms to tackle different problem classes. LP problems are handled with simplex and interior-point methods; MILP problems use branch-and-cut with cutting planes and heuristics; QP and QCP problems are supported via appropriate solver techniques. The package includes presolve routines to simplify models, robust numerical handling, and parallel processing to speed computation on multi-core systems.

History and ecosystem: CPLEX originated with CPLEX Optimization, Inc., and was acquired by IBM in 2009. Since then, it has been integrated into IBM’s portfolio as part of the IBM ILOG CPLEX Optimization Studio. It remains a widely used tool in both academia and industry for modeling and solving complex optimization problems.