SDP Relaxation

SDP (Semidefinite Programming) relaxation is a mathematical technique used to approximate complex optimization problems that are difficult to solve directly. It involves transforming the original problem into a related, simpler one by replacing challenging constraints with relaxed, semidefinite constraints—meaning the solution matrices are constrained to be positive semidefinite. This relaxation makes the problem convex, allowing efficient algorithms to find an approximate solution. Although it may not provide the exact answer, SDP relaxation offers a practical way to obtain good, near-optimal solutions in fields like machine learning, control, and signal processing.