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Accelerated Optimization With Orthogonality Constraints
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We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness of our method, we perform numerical experiments which demonstrate that the number of iterations scales with the square root of the condition number, and also compare with existing state-of-the-art quasi-Newton methods on the Stiefel manifold. Our experiments show that our method outperforms existing state-of-the-art quasi-Newton methods on some large, ill-conditioned problems.
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Quantum Optimization via Gradient-Based Hamiltonian Descent
Gradient-based QHD, a quantum Hamiltonian descent variant that inserts the gradient into the kinetic term, is claimed to converge at O(t^-2) in theory and to outperform QHD and classical methods in 2D tests.
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