Quadratic Constrained Quadratic Programming

Quadratic Constrained Quadratic Programming (QCQP) focuses on solving optimization problems where both the objective function and constraints are quadratic. Current research emphasizes developing efficient algorithms for large-scale QCQPs, exploring novel approaches like hypergraph-based neural networks and projection-based unsupervised learning to improve solution speed and reliability, particularly for semi-definite constraints. These advancements are impacting diverse fields, including autonomous driving (for optimal speed planning) and signal processing (e.g., beamforming optimization), by enabling the solution of previously intractable problems. The development of robust and scalable QCQP solvers is crucial for advancing these and other applications.