The QCQP Approach: A Novel Design Strategy for Optical Computing Devices
Published:
This project explores a novel approach to wave-based optimization problems with high computational complexity (e.g., designing an optical computer). Such devices have potential to alleviate the AI energy crisis by performing matrix multiplication with high efficiency. In MATLAB, I created a Green’s function-based simulation of the device. Then I derived and implemented the traditional adjoint state method of optimization, using it to confirm gradient descent’s tendency to terminate at low-quality local optima in wave-based problems. Next, I reformulated (“lifted”) the optimization problem in matrix form as a quadratically-constrained quadratic program (QCQP). Via semidefinite relaxation, I transformed the QCQP into a computationally easier problem (an SDP) that produces fundamental bounds on performance but physically infeasible designs. With these SDP bounds, I experimented with the true QCQP formulation, finding that the QCQP produces physically feasible, near-globally optimal designs more reliably than traditional gradient-based approaches. Yale nominated this work for the Goldwater Scholarship in Fall 2024.