Semidefinite Programming

Semidefinite programming (SDP) is a powerful optimization technique used to solve complex problems by relaxing them into convex formulations, often involving positive semidefinite matrices. Current research focuses on improving the scalability of SDP solvers, particularly for high-dimensional problems arising in machine learning and robotics, through techniques like low-rank factorization and exploiting problem structure (e.g., chordal sparsity). These advancements enable applications in diverse areas such as neural network verification, robust planning under uncertainty, and efficient algorithms for graph clustering and other combinatorial optimization problems, ultimately leading to more reliable and efficient solutions for a wide range of scientific and engineering challenges.