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

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

The adaptive cubic regularization algorithm employing the inexact gradient and Hessian is proposed on general Riemannian manifolds, together with the iteration complexity to get an approximate second-order optimality under certain…

Fragmentation methods applied to multireference wave functions constitute a road towards the application of highly accurate ab initio wave function calculations to large molecules and solids. However, it is important for reproducibility and…

Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…

Derivative-free Riemannian optimization (DFRO) aims to minimize an objective function using only function evaluations, under the constraint that the decision variables lie on a Riemannian manifold. The rapid increase in problem dimensions…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

Locality of compact one-electron orbitals expanded strictly in terms of local subsets of basis functions can be exploited in density functional theory (DFT) to achieve linear growth of computation time with systems size, crucial in…

Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set…

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, including mixed-precision quantization, non-uniform pruning, and expert selection. The objective, typically model loss, depends…

We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…

In this paper, we develop two Riemannian stochastic smoothing algorithms for nonsmooth optimization problems on Riemannian manifolds, addressing distinct forms of the nonsmooth term \( h \). Both methods combine dynamic smoothing with a…

Computing Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to…

This work explores the global optimization problem of finding lowest-energy configurations (ground states) in disordered continuous spins models from statistical physics, with a particular focus on the random field XY model. Due to an…

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…

We present an efficient orbital optimization procedure that combines the highly GPU accelerated, spin-adapted density matrix renormalization group (DMRG) method with the complete active space self-consistent field (CAS-SCF) approach for…

We propose a Riemannian optimization approach for computing low-rank solutions of the algebraic Riccati equation. The scheme alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is on the set of…

We study global optimization (GOP) in the framework of non-linear inverse problems with a unique solution. These problems are in general ill-posed. Evaluation of the objective function is often expensive, as it implies the solution of a…

In this paper, we study min-max optimization problems on Riemannian manifolds. We introduce a Riemannian Hamiltonian function, minimization of which serves as a proxy for solving the original min-max problems. Under the Riemannian…