SDP (Semi-definite Programming)

Semi-definite programming (SDP) is an advanced optimization technique used to find the best solution within certain constraints, where the variables are represented as matrices that must be positive semi-definite (meaning they have no negative eigenvalues). Think of it as a way to optimize complex problems—such as designing systems, machine learning, or control theory—by ensuring solutions meet specific stability and positivity conditions. SDP generalizes linear programming and can handle more intricate relationships, making it a powerful tool for solving problems that involve matrix variables and require maintaining certain positive properties.