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The IBM Optimization Subroutine Library (OSL) was developed to provide practitioners with a suite of tools for manipulating the mathematical models and solving the resulting minimization and maximization problems of mathematical optimization. The problems that OSL addresses include linear, quadratic, mixed-integer, and pure network programming problems. Individual OSL components implement state-of-the-art algorithms in code that takes advantage of the characteristics of the IBM platforms on which they run. OSL includes solver modules based on the classical simplex method and on newer interior point methods. The OSL components can be combined into applications as simple as "input, call, solver, output" sequences or into complicated, individualized algorithms that have been highly customized by knowledgeable users.