IBM ILOG CPLEX is a high-performance mathematical programming solver for linear, mixed-integer, quadratic, and constraint programming. CPLEX employs state-of-the-art algorithms: dual simplex, barrier method for LP; branch-and-cut for MIP; specialized algorithms for network flows and quadratic programs. Advanced features: automatic problem preprocessing, parallel optimization, solution pool for multiple optima, conflict analysis for infeasible models, and tuning tool for parameter optimization. CPLEX interfaces with modeling languages (AMPL, GAMS), programming languages (C++, Java, Python), and provides Concert Technology API for embedded applications. Industry standard for large-scale optimization in logistics, finance, manufacturing, and telecommunications.