The Active Set Method is an iterative optimization algorithm used to solve constrained optimization problems by maintaining and updating a set of constraints that are considered 'active' at each iteration. It efficiently handles problems with inequality constraints by iteratively solving a series of equality-constrained subproblems, adjusting the active set until convergence to an optimal solution is achieved.

Active Set Method

iterative optimization algorithm

constrained optimization problems

set of constraints

Active constraints

Inequality constraints are conditions that specify a range of permissible values for decision variables in optimization problems, typically expressed in the form of inequalities. They are crucial in ensuring that solutions adhere to real-world limitations such as resource availability, safety standards, or regulatory requirements.

inequality constraints

equality-constrained subproblems

An optimal solution is the best possible outcome that satisfies all constraints in a given problem, often found using optimization techniques. It is crucial in various fields such as mathematics, economics, and computer science, where it helps in decision-making and resource allocation to achieve maximum efficiency or minimum cost.

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