Semidefinite Programming

Semidefinite programming (SDP) is a powerful mathematical optimization method used to find the best solution within certain constraints. It involves optimizing (maximizing or minimizing) a linear function while ensuring that a related matrix remains positive semidefinite—meaning it has no negative eigenvalues. This technique is widely applied in fields like control systems, finance, and machine learning to solve complex problems such as resource allocation, signal processing, and graph theory. Essentially, SDP helps efficiently identify optimal solutions when dealing with issues expressed through matrix inequalities.