MINOS, widely used mathematical software package for solving linear and nonlinear optimization problems. The Modular In-core Nonlinear Optimization System is written in the Fortran programming language.
Professors Bruce Murtagh and Michael Sanders developed MINOS in the 1970s at Stanford University’s Systems Optimization Laboratory in the Department of Operations Research. In 1985, Sanders received the inaugural Orchard-Hays prize from the Mathematical Programming Society for his work on the groundbreaking system.
With its versatile array of algorithms, MINOS stands as a robust solution for a range of optimization problems, including:
Linear programming problems: MINOS employs the simplex method in programming scenarios where both the objective function and constraints exhibit linearity. The simplex method traverses the feasible region of the problem space through a series of vertex-to-vertex movements, iteratively improving the objective function value until an optimal solution is reached. This method is renowned for its effectiveness in solving linear programming problems and is a cornerstone of MINOS’s capability.
Nonlinear objective functions with linear constraints: MINOS leverages a reduced-gradient method when faced with optimization problems characterized by a nonlinear objective function alongside linear constraints. This technique involves updating the search direction based on gradients, guiding the algorithm towards the optimal solution while considering the linear constraints. By efficiently navigating the problem space using reduced gradients, MINOS can converge towards optimal solutions even in the presence of nonlinearities in the objective function.
Problems with nonlinear constraints: For optimization problems featuring nonlinear constraints, MINOS employs the projected Lagrangian method. This approach entails linearizing the nonlinear constraints and formulating an augmented Lagrangian function. MINOS can systematically address the constraints by incorporating Lagrange multipliers while optimizing the objective function. However, it’s important to note that MINOS may exhibit reduced efficiency for highly nonlinear constraints compared to solvers utilizing Sequential Quadratic Programming (SQP) algorithms.
With its diverse algorithmic toolkit, MINOS offers a reliable and versatile platform for solving various optimization problems. Despite its age, MINOS remains valuable for researchers, practitioners, and decision-makers seeking to optimize complex systems and processes across diverse domains.