MINOS (optimization software)

MINOS is a software package designed for solving large-scale optimization problems, particularly those involving sparse linear and nonlinear constraints and a smooth objective function. It is primarily used for solving problems formulated as linearly constrained optimization problems, nonlinear programs (NLP), and mixed integer nonlinear programs (MINLP), often utilizing techniques related to sequential quadratic programming (SQP).

Developed originally at Stanford University, MINOS is a powerful and efficient tool frequently employed in various fields, including engineering, economics, and operations research. Its robust algorithms are suitable for problems with many variables and constraints, making it applicable to real-world scenarios requiring sophisticated optimization techniques.

MINOS employs a reduced-gradient method in conjunction with a quasi-Newton algorithm for handling nonlinearities in the objective function and constraints. This approach efficiently searches for an optimal solution by iteratively improving a feasible point while satisfying the problem's constraints. A key feature of MINOS is its ability to exploit sparsity in the problem's structure, leading to significant computational advantages when dealing with large-scale models.

The software requires a user-provided formulation of the optimization problem, including the objective function, constraints, and variable bounds. MINOS then utilizes its internal algorithms to identify an optimal or near-optimal solution, providing valuable insights for decision-making and problem-solving. It is often integrated into larger modeling systems and can be called from various programming languages. It's a historically significant piece of optimization software that contributed to the field of large-scale optimization.