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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Cong Sun Yaxiang Yuan State Key Laboratory of Scientific and Engineering Computing ICMSEC AMSS Chinese Academy and Sciences Beijing China

A sequential quadratic programming (SQP) method is pro posed to solve the distributed beamforming problem in multiple relay networks. The problem is formulated as the minimization of the total relay transmit power, subject to individual signal-to-interference-and-noise ratio constraints at each receiver, which is a nonconvex quadratic constraint quadratic programming. Rather than solving its semi-definite programming (SDP) relaxation, we apply the SQP method to solve its tightened form to replace its inequality constraints with equalities. Its global convergence is guaranteed. Simulations show that it not only runs much faster, but also performs as good as SDP for calculation results.

关键词： Relays Array signal processing Quadratic programming Interference Signal to noise ratio Peer to peer computing

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A New Fully Polynomial Time Approximation Scheme for the Interval Subset Sum Problem

arXiv

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arXiv 2017年

作者： Diao, Rui Liu, Ya-Feng Dai, Yu-Hong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The interval subset sum problem (ISSP) is a generalization of the well-known subset sum problem. Given a set of intervals {[ai,1, ai,2]}ni=1 and a target integer T, the ISSP is to find a set of integers, at most one from each interval, such that their sum best approximates the target T but cannot exceed it. In this paper, we first study the computational complexity of the ISSP. We show that the ISSP is relatively easy to solve compared to the 0-1 Knapsack problem (KP). We also identify several subclasses of the ISSP which are polynomial time solvable (with high probability), albeit the problem is generally NP-hard. Then, we propose a new fully polynomial time approximation scheme (FPTAS) for solving the general ISSP problem. The time and space complexities of the proposed scheme are O (n max {1/ǫ, log n}) and O (n + 1/ǫ), respectively, where ǫ is the relative approximation error. To the best of our knowledge, the proposed scheme has almost the same time complexity but a significantly lower space complexity compared to the best known scheme. Both the correctness and efficiency of the proposed scheme are validated by numerical simulations. In particular, the proposed scheme successfully solves ISSP instances with n = 100, 000 and ǫ = 0.1% within one second. Copyright © 2017, The Authors. All rights reserved.

关键词： Computational complexity

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Elastic Full Waveform Inversion Based on the Trust Region Strategy

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American Journal of Computational Mathematics 2021年第4期11卷 241-266页

作者： Wensheng Zhang Yijun Li State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China School of Mathematical Sciences University of Chinese Academy Sciences Beijing China

In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually, the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.

关键词： Elastic Wave Equations Full-Waveform Inversion Trust Region Strate-gy Line Search Strategy Newton-Type Method Time Domain

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Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

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Communications on Applied Mathematics and Computation 2024年第1期6卷 30-63页

作者： Maohui Lyu Vrushali A.Bokil Yingda Cheng Fengyan Li State Key Laboratory of Scientific and Engineering Computing(LSEC) Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing100190China Department of Mathematics College of ScienceOregon State UniversityCorvallisOR97331USA Department of Mathematics Michigan State UniversityEast LansingMI48824USA Department of Computational Mathematics Science and EngineeringMichigan State UniversityEast LansingMI48824USA Department of Mathematical Sciences Rensselaer Polytechnic InstituteTroyNY12180USA

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational *** the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the *** main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order *** with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel *** evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

关键词： Maxwell’s equations Kerr and Raman Discontinuous Galerkin method Energy stability

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OPTIMIZATION ON PRODUCT MANIFOLDS UNDER A PRECONDITIONED METRIC

arXiv

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arXiv 2023年

作者： Gao, Bin Peng, Renfeng Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

Since optimization on Riemannian manifolds relies on the chosen metric, it is appealing to know that how the performance of a Riemannian optimization method varies with different metrics and how to exquisitely construct a metric such that a method can be accelerated. To this end, we propose a general framework for optimization problems on product manifolds endowed with a preconditioned metric, and we develop Riemannian methods under this metric. Generally, the metric is constructed by an operator that aims to approximate the diagonal blocks of the Riemannian Hessian of the cost function. We propose three specific approaches to design the operator: exact block diagonal preconditioning, left and right preconditioning, and Gauss–Newton type preconditioning. Specifically, we tailor new preconditioned metrics and adapt the proposed Riemannian methods to the canonical correlation analysis and the truncated singular value decomposition problems, which provably accelerate the Riemannian methods. Additionally, we adopt the Gauss–Newton type preconditioning to solve the tensor ring completion problem. Numerical results among these applications verify that a delicate metric does accelerate the Riemannian optimization *** Codes 15A69, 65K05, 65F30, 90C30 Copyright © 2023, The Authors. All rights reserved.

关键词： Cost functions

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A penalty-free infeasible approach for a class of nonsmooth optimization problems over the Stiefel manifold

arXiv

引用

arXiv 2021年

作者： Xiao, Nachuan Liu, Xin Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. For smooth and 2,1-norm regularized cases, these infeasible approaches adopt simple and orthonormalizationfree updating schemes and show high efficiency in some numerical experiments. However, to avoid orthonormalization while enforcing the feasibility of the final solution, these infeasible approaches introduce a quadratic penalty term,where an inappropriate penalty parameter can lead to numerical inefficiency. Inspired by penalty-free approaches for smooth optimization problems, we proposed a sequential linearized proximal gradient method (SLPG) for a class of optimization problems with orthogonality constraints and nonsmooth regularization term. This approach alternatively takes tangential steps and normal steps to improve the optimality and feasibility respectively. In SLPG, the orthonormalization process is invoked only once at the last step if high precision for feasibility is needed, showing that main iterations in SLPG are orthonormalization-free. Besides, both the tangential steps and normal steps do not involve the penalty parameter, and thus SLPG is penaltyfree and avoids the inefficiency caused by possible inappropriate penalty parameter. We analyze the global convergence properties of SLPG where the tangential steps are inexactly computed. By inexactly computing tangential steps, for smooth cases and 2,1-norm regularized cases, SLPG has a closed-form updating scheme, which leads to cheap tangential steps. Numerical experiments illustrate the advantages of SLPG when compared with existing first-ordermethods. Copyright © 2021, The Authors. All rights reserved.

关键词： Gradient methods

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A Smoothing Levenberg-Marquardt Type Method for NCP

A Smoothing Levenberg-Marquardt Type Method for NCP

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第四届运筹学及其应用国际研讨会

作者： Ju-Liang Zhang State Key Laboratory of Science and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and System SciencesChinese Academy of Sciences

＜正＞In this paper,we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg-Marquardt type method to solve the nonlinear equation *** global and local superlinear convergence properties of the method are obtained under very mild ***,the algorithm is locally super-linearly convergent without assumption of strict complementarity of the solutions and uniqueness of the solution of NCP.

关键词： NCP Levenberg-Marquardt method smoothing technique P0 matrix superlinear convergence

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Car-Parinello molecular dynamics simulations of thionitroxide and S-nitrosothiol in the gas phase,methanol,and water——A theoretical study of S-nitrosylation

引用

中国科学:化学 2012年第10期42卷 1497-1498页

作者： LIANG Juan1,CHENG ShangLi1,HOU JunWei1,XU ZhenHao1,2 & ZHAO Yi-Lei1,2,3* 1 state key laboratory of Microbial Metabolism,School of Life Sciences and Biotechnology,Shanghai Jiao Tong University,Shanghai 200240,China 2 Shanghai Center for Systems Biomedicine,Shanghai Jiao Tong University,Shanghai 200240,China 3 MOE laboratory of scientific and engineering computing,Shanghai Jiao Tong University,Shanghai 200240,China State Key Laboratory of Microbial Metabolism School of Life Sciences and Biotechnology Shanghai Jiao Tong University Shanghai 200240 China Shanghai Center for Systems Biomedicine Shanghai Jiao Tong University Shanghai 200240 China MOE Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China

A dilemma about whether thionitroxide radical(RSNHO) or S-nitrosothiol(RSNO) is observed in protein S-nitrosylation has arisen *** illustrate the effect of chemical environment on these structures,this paper presents quantum mechanical molecular dynamics of thionitroxide,and cis-and trans-S-nitrosothiols in the gas phase,methanol,and *** using Car-Parrinello molecular dynamics(CPMD),we have observed that there is free rotation about the S-N bond at 300 K in thionitroxide,but no such rotation is observed for *** C-S-N-O torsion angle distribution in thionitroxide is significantly dependent upon the surrounding environment,leading to either gauche-,cis-,or *** the case of S-nitrosothiol the C-S-N-O plane is twisted slightly by 5°-15° in the cis-isomer,while the periplanar structure is well-retained in the *** calculated results are in agreement with the X-ray crystallographic data of small molecular RSNO ***,for both compounds,the CPMD simulations show that solvation can cause a decrease in the S-N bond ***,the oxygen atom of thionitroxide is found to be a good hydrogen-bond acceptor,forming an oxyanion-hole-like hydrogen bonding network.

关键词： quantum mechanical molecular dynamics S-nitrosylation thionitroxide S-nitrosothiol solvent effect

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Flexible alignment of images using B-spline reparameterization and L2-gradient flows

Flexible alignment of images using B-spline reparameterizati...

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Congress on Image and Signal Processing, CISP

作者： Guoliang Xu Yanmei Zheng State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Chinese Academy and Sciences Beijing China

In this paper, we present a new flexible alignment method to align two or more similar images. By minimizing an energy functional measuring the difference of the initial image and target image, a L 2 -gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and a semi-implicit Euler scheme in the temporal direction. The experimental results show that the proposed method is efficient, effective and capable of capturing large variation of the initial and the target images.

关键词： Spline Image registration Linear systems Correlation Equations

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Adaptive energy-preserving algorithms for guiding center system

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Plasma Science and Technology 2023年第4期25卷 11-22页

作者：朱贝贝刘健张嘉炜祝爱卿唐贻发 Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083Peopleʼs Republic of China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026Peopleʼs Republic of China Advanced algorithm Joint Lab Shandong Computer Science CenterQilu University of TechnologyJinan 250014Peopleʼs Republic of China The State Key Laboratory of Scientific and Engineering Computing The Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190Peopleʼs Republic of China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049Peopleʼs Republic of China

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized *** adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving *** new adaptive algorithms are second order,and their algebraic order is carefully *** results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

关键词： guiding center system energy-preserving methods adaptive energy conservation

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