arXiv subjects

Xin Qu

Publications and source records attributed to Xin Qu.

7 recordsLinked to original sources

arXiv2026

An Anderson-accelerated stochastic extragradient method for stochastic variational inequalities

In this paper, we propose an Anderson-accelerated stochastic extragradient algorithm for solving a class of stochastic variational inequalities, by incorporating Anderson acceleration into the stochastic extragradient method under a stochastic approximation framework. A key challenge in our setting is that the pseudomonotonicity assumption is only imposed on the expectation of the stochastic operator, rather than on the individual stochastic operator itself and the sample averages utilized in the algorithm. We prove that, despite the lack of pseudomonotonicity in the sampled operators, the sequence generated by the proposed algorithm converges almost surely to a solution of the stochastic variational inequality problem. Additionally, we establish the sublinear convergence rate of the proposed algorithm in terms of the mean residual function, along with its optimal oracle complexity. Finally, we validate the effectiveness of the proposed algorithm through numerical experiments.

math.OC↗

arXiv2024

An extra gradient Anderson-accelerated algorithm for pseudomonotone variational inequalities

This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to have fast convergent rate. We prove that the sequence generated by the proposed algorithm from any initial point converges to a solution of the pseudomonotone variational inequality problem without assuming the Lipschitz continuity and contractive condition, which are used for convergence analysis of the extra gradient method and Anderson-accelerated method, respectively in existing literatures. Numerical experiments, particular emphasis on Harker-Pang problem, fractional programming, nonlinear complementarity problem and PDE problem with free boundary, are conducted to validate the effectiveness and good performance of the proposed algorithm comparing with the extra gradient method and Anderson-accelerated method.

math.OC↗

arXiv2022

Density functional theory plus dynamical mean field theory within the framework of linear combination of numerical atomic orbitals: Formulation and benchmarks

The combination of density functional theory with dynamical mean-field theory (DFT+DMFT) has become a powerful first-principles approach to tackle strongly correlated materials in condensed matter physics. The wide use of this approach relies on robust and easy-to-use implementations, and its implementation in various numerical frameworks will increase its applicability on the one hand and help crosscheck the validity of the obtained results on the other. In the work, we develop a formalism within the linear combination of numerical atomic orbital (NAO) basis set framework, which allows for merging NAO-based DFT codes with DMFT quantum impurity solvers. The formalism is implemented by interfacing two NAO-based DFT codes with three DMFT impurity solvers, and its validity is testified by benchmark calculations for a wide range of strongly correlated materials, including 3\textit{d} transition metal compounds, lanthanides, and actinides. Our work not only enables DFT+DMFT calculations using popular and rapidly developing NAO-based DFT code packages, but also facilitates the combination of more advanced beyond-DFT methodologies available in this codes with the DMFT machinery.

cond-mat.str-el↗

arXiv2022

DFT+$U$ within the framework of linear combination of numerical atomic orbitals

We present a formulation and implementation of the DFT+\textit{U} method within the framework of linear combination of numerical atomic orbitals (NAO). Our implementation not only enables single-point total energy and electronic-structure calculations but also provides access to atomic forces and stresses, hence allowing for full structure relaxations of periodic systems. Furthermore, our implementation allows one to deal with non-collinear spin texture, with the spin-orbit coupling (SOC) effect treated self-consistently. The key aspect behind our implementation is a suitable definition of the correlated subspace when multiple atomic orbitals with the same angular momentum are used, and this is addressed via the "Mulliken charge projector" constructed in terms of the first (most localized) atomic orbital within the $d/f$ angular momentum channel. The important Hubbard $U$ and Hund $J$ parameters can be estimated from a screened Coulomb potential of the Yukawa type, with the screening parameter either chosen semi-empirically or determined from the Thomas-Fermi screening model. Benchmark calculations are performed for four late transition metal monoxide bulk systems, i.e., MnO, FeO, CoO, and NiO, and for the 5$d$-electron compounds IrO$_2$. For the former type of systems, we check the performance of our DFT+$U$ implementation for calculating band gaps, magnetic moments, electronic band structures, as well as forces and stresses; for the latter, the efficacy of our DFT+$U$+SOC implementation is assessed. Systematic comparisons with available experimental results, and especially with the results from other implementation schemes are carried out, which demonstrate the validity of our NAO-based DFT+$U$ formalism and implementation.

cond-mat.mtrl-sci↗

arXiv2021

Fast inertial dynamic algorithm with smoothing method for nonsmooth convex optimization

In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic behavior of the dynamic algorithm, we prove that each trajectory of it weakly converges to an optimal solution under some appropriate conditions on the smoothing parameters, and the convergence rate of the objective function values is o(t^-2). We also show that the algorithm is stable, that is, this dynamic algorithm with a perturbation term owns the same convergence properties when the perturbation term satisfies certain conditions. Finally, we verify the theoretical results by some numerical experiments.

math.OC↗

arXiv2020

A Closed-form Transceiver Design for Interference Alignment and Cancellation (IAC) in MIMO Interference Channel

For a K-user interference channel, the degree of freedom (DoF) which can be achieved through interference alignment (IA) is constrained to signal space dimension governed by the number of Tx/Rx antennas. To overcome this problem, IA can be combined with interference cancellation (IC), involving a new receiver architecture associated with signaling over backhaul links among the different users, as another interference mitigation scheme which is referred to as interference alignment and cancellation (IAC). In our earlier work, by proposing an IAC graph, we have derived the necessary and sufficient conditions for the existence of closed-form solutions for IAC subject to the given DoF requirement for individual user. Furthermore, we have also shown that it can achieve the theoretically maximum possible DoF, which is 2M for MIMO system with M Tx/Rx antennas. Following our previous works on IAC, we aim to investigate the design criteria to obtain such closed-form transceivers when they exist. We first develop a general closed-form IAC transceiver design for any given DoF requirement of individual user and then, we specify how the optimal IAC transceiver can be designed to achieve the theoretically maximum DoF of 2M, beating the performance of conventional IA with much less computational complexity.

eess.SP↗

arXiv2018

A hierarchical statistical framework for emergent constraints: application to snow-albedo feedback

Emergent constraints use relationships between future and current climate states to constrain projections of climate response. Here, we introduce a statistical, hierarchical emergent constraint (HEC) framework in order to link future and current climate with observations. Under Gaussian assumptions, the mean and variance of the future state is shown analytically to be a function of the signal-to-noise (SNR) ratio between data-model error and current-climate uncertainty, and the correlation between future and current climate states. We apply the HEC to the climate-change, snow-albedo feedback, which is related to the seasonal cycle in the Northern Hemisphere. We obtain a snow-albedo-feedback prediction interval of $(-1.25, -0.58)$ \%$K^{-1}$. The critical dependence on SNR and correlation shows that neglecting these terms can lead to bias and under-estimated uncertainty in constrained projections. The flexibility of using HEC under general assumptions throughout the Earth System is discussed.

physics.ao-ph↗