Semidefinite Programming (SDP) is a type of optimization problem where the goal is to maximize or minimize a linear function subject to constraints that require a matrix to be semidefinite. A matrix is semidefinite if all its eigenvalues are non-negative, which means it does not "bend" in a negative direction. This property makes SDP useful in various fields, including control theory, combinatorial optimization, and machine learning. SDP can be seen as a generalization of linear programming, where instead of dealing with linear inequalities, it involves matrix inequalities. It is particularly effective for problems that can be represented in terms of quadratic forms, such as those found in graph theory and signal processing. The development of efficient algorithms for solving SDP has significantly advanced its applications in both theoretical and practical scenarios.