Cutting plane methods is a class of algorithmic techniques employed in mathematical optimization, primarily for solving integer and mixed-integer programming problems. These methods operate by iteratively adding linear inequalities, known as cutting planes or cuts, to a relaxed formulation of the problem (typically a linear programming relaxation). Each cut eliminates non-integer solutions that are optimal for the current relaxation without excluding any feasible integer solutions, thereby progressively reducing the feasible region until an integer optimum is found or the problem is deemed infeasible. The significance of cutting plane methods lies in their ability to leverage continuous optimization techniques to address problems with discrete variable requirements, often forming a core component of more complex algorithms like branch-and-cut.