The Cutting Plane Method is an optimization technique used to solve linear programming problems by iteratively refining a feasible region. By adding linear inequalities, known as cuts, this method incrementally approaches the optimal solution while excluding non-optimal regions of the solution space.

Cutting Plane Method

Optimization technique

Linear programming problems

The feasible region is the set of all possible points that satisfy a given set of constraints in a mathematical optimization problem. It is crucial for determining the optimal solution, as only points within this region can be considered viable candidates for the solution.

Feasible Region

Linear inequalities are mathematical expressions that involve a linear function and use inequality symbols to show the relationship between two expressions. They are used to represent ranges of possible solutions and are fundamental in fields like optimization and economics for decision-making under constraints.

Linear Inequalities

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.

Optimal Solution

Non-optimal regions

Solution space refers to the set of all possible solutions to a given problem, often visualized in optimization and decision-making contexts. It is crucial for understanding the range of potential outcomes and for identifying the optimal solution based on specific criteria or constraints.

Concepts

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