A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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A Riemannian L-BFGS method with adapted Cauchy-point bound handling outperforms classical interior-point and L-BFGS-B solvers on mixed manifold-plus-bounds problems by orders of magnitude.
Introduces natural-gradient versions of Heavy-Ball and Nesterov momentum methods for function approximation on differentiable nonlinear manifolds.
A BCD framework using WMMSE, Riemannian conjugate gradient, and successive convex approximation jointly optimizes dual-aerial RIS phases, precoders, and trajectories in ITNTNs, delivering about 7% higher sum-rate than random RIS in simulations.
Monotonic Basin Hopping outperforms MultiStart for locating lower-energy ground states in the random field XY model after reformulating the Hamiltonian on spheres for Riemannian optimization.
Joint optimization of beamforming, active RIS phases and gains, and 3D trajectories of UAV and HAP in a dual-aerial ARIS NOMA ITNTN yields approximately 8.44% higher average sum-rate than passive RIS benchmarks.
citing papers explorer
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A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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A Riemannian quasi-Newton algorithm for optimization with Euclidean bounds
A Riemannian L-BFGS method with adapted Cauchy-point bound handling outperforms classical interior-point and L-BFGS-B solvers on mixed manifold-plus-bounds problems by orders of magnitude.
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Natural gradient descent with momentum
Introduces natural-gradient versions of Heavy-Ball and Nesterov momentum methods for function approximation on differentiable nonlinear manifolds.
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Joint Trajectory and Resource Optimization for Aerial RIS-assisted Integrated TNT Networks
A BCD framework using WMMSE, Riemannian conjugate gradient, and successive convex approximation jointly optimizes dual-aerial RIS phases, precoders, and trajectories in ITNTNs, delivering about 7% higher sum-rate than random RIS in simulations.
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Nonconvex optimization methods for ground states in disordered continuous-spin models
Monotonic Basin Hopping outperforms MultiStart for locating lower-energy ground states in the random field XY model after reformulating the Hamiltonian on spheres for Riemannian optimization.
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Joint Trajectory and Resource Optimization for Dual-aerial ARIS-assisted NOMA-TNT Networks
Joint optimization of beamforming, active RIS phases and gains, and 3D trajectories of UAV and HAP in a dual-aerial ARIS NOMA ITNTN yields approximately 8.44% higher average sum-rate than passive RIS benchmarks.