相关论文: Geometric Optimization of Restricted-Open and Comp…

Geodesic convexity (g-convexity) is a natural generalization of convexity to Riemannian manifolds. However, g-convexity lacks many desirable properties satisfied by Euclidean convexity. For instance, the natural notions of half-spaces and…

Orbital optimization procedure is widely called in electronic structure simulation. To efficiently find the orbital optimization solution, we developed a new second order orbital optimization algorithm, co-iteration augmented Hessian (CIAH)…

We present the time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory as a new framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock…

Our previously developed Constrained-Pairing Mean-Field Theory (CPMFT) is shown to map onto an Unrestricted Hartree-Fock (UHF) type method if one imposes a corresponding pair constraint to the correlation problem that forces occupation…

In a Hilbert space $H$, in order to develop fast optimization methods, we analyze the asymptotic behavior, as time $t$ tends to infinity, of inertial continuous dynamics where the damping acts as a closed-loop control. The function $f: H…

Many machine learning applications are naturally formulated as optimization problems on Riemannian manifolds. The main idea behind Riemannian optimization is to maintain the feasibility of the variables while moving along a descent…

In this paper, we study symmetry-improved fractional Sobolev embeddings on closed Riemannian manifolds under the action of compact isometry groups. We prove that \(G\)-invariant fractional Sobolev spaces embed into higher \(L^p\) spaces,…

This article deals with optimizing problems classified by the kinds of restrictions as required in differential geometry and in mechanics: holonomic and nonholonomic. The central issue relates to dual nonholonomic programs (what they mean…

This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…

We consider Riemannian inequality-constrained optimization problems. Such problems inherit the benefits of Riemannian approach developed in the unconstrained setting and naturally arise from applications in control, machine learning, and…

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target…

We propose an L-BFGS optimization algorithm on Riemannian manifolds using minibatched stochastic variance reduction techniques for fast convergence with constant step sizes, without resorting to linesearch methods designed to satisfy Wolfe…

In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…

Direct minimization method on the complex Stiefel manifold in Kohn-Sham density functional theory is formulated to treat both finite and extended systems in a unified manner. This formulation is well-suited for scenarios where…

We present Extended Riemannian Stochastic Derivative-Free Optimization (Extended RSDFO), a novel population-based stochastic optimization algorithm on Riemannian manifolds that addresses the locality and implicit assumptions of manifold…

This study presents an evaluation of derivative-free optimization algorithms for the direct minimization of Hartree-Fock-Roothaan energy functionals involving nonlinear orbital parameters and quantum numbers with noninteger order. The…

We introduce in this paper a manifold optimization framework that utilizes semi-Riemannian structures on the underlying smooth manifolds. Unlike in Riemannian geometry, where each tangent space is equipped with a positive definite inner…

Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be…

We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on our search space to the…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…