arXiv:2607. 23642v1 Announce Type: cross Abstract: Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm.
arXiv:2607. 07204v2 Announce Type: replace-cross Abstract: Structured preconditioners restrict optimization to a small family of positive metrics, but endpoint condition-number reachability does not measure the geometric effort required to reach a useful metric.
The paper investigates local stationary solutions of finite‑horizon discrete‑time Pontryagin systems near a steady extremal. Under regularity of the stationarity equation, hyperbolicity of the reduced state–costate map, and a scaled transversality condition, the linearized boundary‑value problem admits a uniformly bounded inverse, leading to existence, uniqueness, and uniform Lipschitz estimates independent of the horizon. The study further shows that perturbations of the terminal reward decay exponentially with the horizon, and for linear‑quadratic systems with suitable conditions the Riccati matrix and initial feedback gain converge at a quantified rate, with numerical experiments confirming the theoretical predictions.
arXiv:2605. 07116v2 Announce Type: replace Abstract: We analyze a neural semi-discrete method for high-dimensional first-order Hamilton-Jacobi-Bellman (HJB) equations with known or learned dynamics.
arXiv:2607. 13943v1 Announce Type: cross Abstract: Inspired by interior-point methods (IPM) for structured convex optimization, Kannan and Narayanan introduced the Dikin walk for sampling uniformly from polytopes in 2009.
While entropy regularization is widely used to stabilize and accelerate Natural Policy Gradient methods, its ability to yield faster convergence rates for the unregularized objective remains underexplored. Existing analyses often rely on double-loop architectures and invoke a linear entropy penalty.
arXiv:2607. 03503v1 Announce Type: new Abstract: Graph-based semi-supervised learning (SSL) propagates a few labels over a similarity graph by minimizing a Dirichlet-type energy.
arXiv:2609. 20701v1 Announce Type: cross Abstract: We study efficient algorithms for realizing the first-order oracle complexity of optimization of $G$-Lipschitz convex functions with respect to the $\ell_{q}$-norm over an $\ell_{p}$-ball of radius $R$, where $1\leq p,q\leq \infty$.
arXiv:2605. 23391v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) for coupled multiphysics systems suffer systematic accuracy degradation as inter-equation coupling strengthens.
arXiv:2609. 21880v1 Announce Type: cross Abstract: We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$.
arXiv:2606. 04031v1 Announce Type: new Abstract: Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training.
arXiv:2607. 06723v1 Announce Type: cross Abstract: Most gradient-based optimization methods move parameters through a fixed background geometry, even when their internal states implicitly define changing notions of length, curvature, and preconditioning.
arXiv:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.