Parabolic Relaxation

Parabolic relaxation is a technique used to approximate solutions to difficult non-convex optimization problems, particularly those arising in quadratically constrained quadratic programming (QCQP) and related areas like reinforcement learning and formal verification. Current research focuses on developing efficient algorithms for implementing parabolic relaxation, including adaptations of gradient descent methods and the exploration of tight relaxations that minimize the gap between the approximation and the true solution. This approach offers significant potential for improving the speed and accuracy of solving complex optimization problems across diverse fields, from robotics and machine learning to neural network verification and multigrid methods.