quasi-Newton Iteration Research Articles

REVEAL: A Global Full-Waveform Inversion Model

ABSTRACT We present REVEAL, a global-scale, transversely isotropic full-waveform inversion model. REVEAL builds upon the earlier construction of the long-wavelength Earth (LOWE) model by lowering the minimum period from 100 to 33 s and by more than doubling the number of included earthquakes to 2366. In the course of 305 quasi-Newton iterations, REVEAL assimilated a total of 6,005,727 unique three-component waveforms. The inversion method rests on the combination of a stochastic mini-batch optimization and wavefield-adapted spectral-element meshes. Although the former naturally exploits redundancies in the data set, the latter reduces the cost of wavefield simulations by reducing the effective dimension of the numerical mesh. As a consequence, the average cost of an iteration in this inversion is only around 0.62% of an iteration that uses the complete data set with a standard cubed-sphere-type mesh. We calculated 3D synthetic seismograms using a graphics processing unit-accelerated spectral-element wave propagation solver, accommodating the effects of anelasticity, topography, bathymetry, ocean loading, and ellipticity. For a diverse range of global wavepaths, REVEAL predicts complete three-component seismograms at 33 s period that have not been included in the inversion. This generalization to unseen data suggests applications of REVEAL in event location and characterization, as well as in ground-motion modeling.

Calculation of ship floating state by quasi-Newton iteration method for onboard loading computer

ABSTRACT Calculating the floating state of a ship is the basic function of onboard loading computer, which is crucial for ship safety. Aiming at the deficiencies in the existing algorithms, we used the quasi-Newton iteration method to calculate the floating state of a ship. Firstly, the section model database of ship's hull was established by cutting the stereolithographic (STL) 3D model which is created by ship design software. Then, Sutherland–Hodgma polygon clipping algorithm and Shoelace Formula were used to calculate the Jacobian matrix. Finally, We selected a 108,000 DWT bulk carrier, ADMIRAL SCHMIDT, as an example to verify the correctness of the algorithm. We performed 100,000 random loading numerical tests, the average number of iterations was 2–3, and the number of convergence failures was zero. We calculated 24 typical standard loading conditions. We found the maximum average absolute error of the draught and trim were 0.0081 and −0.0283 m, respectively. The calculation error was far less than the requirements of the classification society. The results showed that the Quasi-Newton iteration method is simple to implement and easy to program, and has high robustness and accuracy and appropriate convergence. The method is suitable for the real-time calculation of a ship's floating state and has considerable engineering application value.

A spectral iterative algorithm for solving constrained optimal control problems with nonquadratic functional

The numerical approximation of the solution to Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs) in constrained optimal control problems (COCPs) with nonquadratic functional is studied in this investigation. Discretizing both of the space and time of HJB PDE by the Legendre collocation method, a nonlinear system of algebraic equations is obtained to find the expansion coefficients of the approximate solution. However, solving the system of nonlinear algebraic equations is generally relatively difficult and time-consuming. To improve the implementation of the method, we combine the Legendre collocation method with the policy iteration (PI) algorithm. This process leads to a sequence of linear systems of algebraic equations to find the expansion coefficients. The convergence results for the proposed method are provided. Moreover, it is shown that the PI algorithm for a class of constrained optimal control problems with odd nonquadratic functionals is mathematically equivalent to the quasi-Newton's iteration. Finally, the efficiency and accuracy of the method are demonstrated by solving a number of examples.

An Efficient Signal Detection Method Based on Enhanced Quasi-Newton Iteration for Massive MIMO Systems

An Efficient Signal Detection Method Based on Enhanced Quasi-Newton Iteration for Massive MIMO Systems

Real-time modeling of transient behavior of the primary coolant system in pool-type sodium cooled fast reactor

In the paper, a real-time simulation code THCSA-RT is developed to analyze the primary coolant system of pool-type sodium cooled fast reactor which includes reactor core, hot and cold sodium pools, pumps, and intermediate heat exchangers. Different numerical methods including Gear multi-value method and Quasi-Newton iteration method are used to solve the mass and energy equations set and the momentum equations set, respectively. Several typical design basis conditions of CEFR such as planned shutdown condition and RIA are analyzed, and the calculation results agree well with those of the final safety analysis report calculated by DINROS. The simulation time is presented to prove the effectiveness of the new numerical methods developed in the present work, and the new numerical methods could be applied in the similar system analysis codes as well. The newly developed code THCSA-RT could be used in the system real-time simulation of pool-type sodium cooled fast reactor and has been adopted in the development of CEFR full scope simulator.

Realization of Accurate Modeling and Simulation of Oilfield Water Mixing Gathering and Transportation System

In order to solve the shortcomings that the simulation accuracy of oilfield water mixing gathering and transportation system is not high, the dual-process of mixing water and returning to the station cannot be realized at the same time, the system is accurately modeled, and the data structure and computer model suitable for calculation are established by reading static data. The design modeling software realizes the logical and data interface and realizes the display of the physical model on the computer. Based on the quasi-Newton loop iteration method, an online algorithm is proposed. Using the flow rate of each node of the system as the constraint condition, the water mixing process node and pipeline parameters are calculated. According to the calculation results and the oil well produced fluid parameters, the principle of mixed calorimetry is applied to construct the initial value and iterative formula of the return flow simulation. The temperature at the return station is consistent with the inlet temperature of the heating furnace at the joint station. It can dynamically reflect the production and operation status of the water mixing system, and provide a scientific basis for the control and operation of the water mixing system.

Isogeometric analysis of multi-patch solid-shells in large deformation

In the context of isogeometric analysis (IGA) of shell structures, the popularity of the solid-shell elements benefit from formulation simplicity and full 3D stress state. However some basic questions remain unresolved when using solid-shell element, especially for large deformation cases with patch coupling, which is a common scene in real-life simulations. In this research, after introduction of the solid-shell nonlinear formulation and a fundamental 3D model construction method, we present a non-symmetric variant of the standard Nitsche’s formulation for multi-patch coupling in association with an empirical formula for its stabilization parameter. An selective and reduced integration scheme is also presented to address the locking syndrome. In addition, the quasi-Newton iteration format is derived as solver, together with a step length control method. The second order derivatives are totally neglected by the adoption of the non-symmetric Nitsche’s formulation and the quasi-Newton solver. The solid-shell elements are numerically studied by a linear elastic plate example, then we demonstrate the performance of the proposed formulation in large deformation, in terms of result verification, iteration history and continuity of displacement across the coupling interface. In the context of isogeometric analysis (IGA), after introduction of the solid-shell nonlinear formulation and a fundamental 3D model construction method, we present a non-symmetric variant of the standard Nitsche’s formulation for multi-patch coupling in association with an empirical formula for its stabilization parameter. An selective and reduced integration scheme is also introduced to address the locking syndrome. In addition, the quasi-Newton iteration format is derived as solver, together with a step length control method. The second order derivatives are totally neglected by the adoption of the non-symmetric Nitsche’s formulation and the quasi-Newton solver. The performance of the proposed formulation in large deformation is demonstrated by several examples.

Microwave Correlation Forward-Looking Super-Resolution Imaging Based on Compressed Sensing

Forward-looking correlated imaging plays an increasingly important role in modern radar imaging systems. It overcomes disadvantages of traditional side or squint synthetic aperture radar (SAR) which is dependent on specific relative motion between the radar and target scene. A new microwave forward-looking correlated 3-D imaging method based on random radiation field combined with sparse reconstruction is proposed in this article. Firstly, phased array radar (PAR) is adopted to form different and random antenna patterns. Then, combined with the compressed sensing (CS) theory, the target image can be recovered with very few samples which can break through Rayleigh resolution limitation. Furthermore, the proposed method can achieve resolution at least 5.5 times higher than real aperture imaging. To raise computation efficiency of sparse reconstruction, an improved quasi-Newton iteration method based on graphics processing unit (GPU) platform is developed. Meanwhile, a GPU-based (NVIDIA Tesla K40c) accelerated computing method can significantly reduce the processing time compared with the time given by a personal computer (PC). Both simulation and field experiment verify the validity of the proposed method.

Solving the Boundary Value Problem of Curves With Prescribed Geodesic Curvature Based on a Cubic B-Spline Element Method

Composite manufacturing processes such as automated tape placement (ATP) and filament winding process (FW) put forward specific requirements for the geodesic curvature along the layup paths of the composite tows and tapes. In this paper, a non-uniform cubic b-spline element method is proposed for solving the boundary value problem of curves with prescribed geodesic curvature. The differential equation system of the target curve is discretized through the point collocation method, and a quasi-Newton iteration scheme is adopted to approach the real solution from an initial approximation. The proposed method is proved to have third order accuracy, which shows more superiorities comparing with existing numerical methods. Simulations and experiments on a series of parametric surfaces are performed to investigate the performance of the proposed approach and the results verify the high efficiency. The proposed method could cope with the BVP for curves no matter their geodesic curvature vanishes or not. At the same time, the computed curves are natural and smooth such that interpolation technique is unnecessary to ensure the continuity of target curves. One potential application of this method is trajectory optimization for automated tape placement process.

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

Global adjoint tomography—model GLAD-M25

SUMMARYBuilding on global adjoint tomography model GLAD-M15, we present transversely isotropic global model GLAD-M25, which is the result of 10 quasi-Newton tomographic iterations with an earthquake database consisting of 1480 events in the magnitude range 5.5 ≤ Mw ≤ 7.2, an almost sixfold increase over the first-generation model. We calculated fully 3-D synthetic seismograms with a shortest period of 17 s based on a GPU-accelerated spectral-element wave propagation solver which accommodates effects due to 3-D anelastic crust and mantle structure, topography and bathymetry, the ocean load, ellipticity, rotation and self-gravitation. We used an adjoint-state method to calculate Fréchet derivatives in 3-D anelastic Earth models facilitated by a parsimonious storage algorithm. The simulations were performed on the Cray XK7 ‘Titan’ and the IBM Power 9 ‘Summit’ at the Oak Ridge Leadership Computing Facility. We quantitatively evaluated GLAD-M25 by assessing misfit reductions and traveltime anomaly histograms in 12 measurement categories. We performed similar assessments for a held-out data set consisting of 360 earthquakes, with results comparable to the actual inversion. We highlight the new model for a variety of plumes and subduction zones.

Localization of a Moving Object With Sensors in Motion by Time Delays and Doppler Shifts

This paper investigates the problem of active localization of a moving object in its initial position and velocity, using time delay only or with Doppler shift measurements acquired by a number of monostatic sensors. Each sensor has non-negligible motion during the observation period, causing it at different positions when it sends and receives the signal, with the separation proportional to the signal travel time in reaching the object and returning back. The object is not at the same position when it reflects the signals from various sensors due to its motion. Both motion effects lead to recursive model equations for time delay and Doppler shift, making the localization problem interesting and challenging. We shall derive the measurement model equations under this scenario, evaluate the Cramer-Rao lower bound (CRLB) of the estimation problem and analyze the proposed models by contrasting with the performance loss when ignoring the object and sensor motion effects. The Maximum Likelihood Estimators (MLEs) are next developed, using the Gauss-Newton or Quasi-Newton iterations. Algebraic solution for the special case of moving object non-moving sensors is derived and analyzed, and it can serve as an effective initialization of the iterative MLEs if sensor motion is present. Both the theoretical analysis and simulation studies corroborate the importance of taking the object and sensor motions into consideration during the observation period, when the relative velocity between the object and sensor is significant compared to the signal propagation speed, such as in an acoustic or underwater environment.

Generalized Uniformly Optimal Methods for Nonlinear Programming

In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search step (gradient descent or Quasi-Newton iteration) into these uniformly optimal convex programming methods, and then enforce a monotone decreasing property of the function values computed along the trajectory. Algorithms of these types will then achieve the best known complexity for nonconvex problems, and the optimal complexity for convex ones without requiring any problem parameters. As a consequence, we can have a unified treatment for a general class of nonlinear programming problems regardless of their convexity and smoothness level. In particular, we show that the accelerated gradient and level methods, both originally designed for solving convex optimization problems only, can be used for solving both convex and nonconvex problems uniformly. In a similar vein, we show that some well-studied techniques for nonlinear programming, e.g., Quasi-Newton iteration, can be embedded into optimal convex optimization algorithms to possibly further enhance their numerical performance. Our theoretical and algorithmic developments are complemented by some promising numerical results obtained for solving a few important nonconvex and nonlinear data analysis problems in the literature.

A new filter QP-free method for the nonlinear inequality constrained optimization problem

In this paper, a filter QP-free infeasible method with nonmonotone line search is proposed for minimizing a smooth optimization problem with smooth inequality constraints. This proposed method is based on the solution of nonsmooth equations, which are obtained by the Lagrangian multiplier method and the function of the nonlinear complementarity problem for the Karush–Kuhn–Tucker optimality conditions. Especially, each iteration of this method can be viewed as a perturbation of a Newton or quasi-Newton iteration on both the primal and dual variables for the solution of the Karush–Kuhn–Tucker optimality conditions. What is more, it is considered to use the function of the nonlinear complementarity problem in the filter, which makes the proposed algorithm avoid the incompatibility. Then the global convergence of the proposed method is given. And under some mild conditions, the superlinear convergence rate can be obtained. Finally, some preliminary numerical results are shown to illustrate that the proposed filter QP-free infeasible method is quite promising.

Modeling Time-Varying Effects With Large-Scale Survival Data: An Efficient Quasi-Newton Approach

ABSTRACTNonproportional hazards models often arise in biomedical studies, as evidenced by a recent national kidney transplant study. During the follow-up, the effects of baseline risk factors, such as patients’ comorbidity conditions collected at transplantation, may vary over time. To model such dynamic changes of covariate effects, time-varying survival models have emerged as powerful tools. However, traditional methods of fitting time-varying effects survival model rely on an expansion of the original dataset in a repeated measurement format, which, even with a moderate sample size, leads to an extremely large working dataset. Consequently, the computational burden increases quickly as the sample size grows, and analyses of a large dataset such as our motivating example defy any existing statistical methods and software. We propose a novel application of quasi-Newton iteration method to model time-varying effects in survival analysis. We show that the algorithm converges superlinearly and is computationally efficient for large-scale datasets. We apply the proposed methods, via a stratified procedure, to analyze the national kidney transplant data and study the impact of potential risk factors on post-transplant survival. Supplementary materials for this article are available online.

A new greedy algorithm for sparse recovery

Abstract Compressed sensing (CS) has been one of the great successes of applied mathematics in the last decade. This paper proposes a new method, combining the advantage of the Compressive Sampling Matching Pursuit (CoSaMP) algorithm and the Quasi–Newton Iteration Projection (QNIP) algorithm, for the recovery of sparse signal from underdetermined linear systems. To get the new algorithm, Quasi–Newton Projection Pursuit (QNPP), the least-squares technique in CoSaMP is used to accelerate convergence speed and QNIP is modified slightly. The convergence rate of QNPP is studied, under a certain condition on the restricted isometry constant of the measurement matrix, which is smaller than that of QNIP. The fast version of QNPP is also proposed which uses the Richardson’s iteration to reduce computation time. The numerical results show that the proposed algorithms have higher recovery rate and faster convergence speed than existing techniques.

Three-dimensional overturned traveling water waves

Traveling gravity-capillary water waves on the interface of a three-dimensional fluid of infinite depth are computed. The vortex sheet formulation with the small scale approximation is used as the mathematical model for the fluid motion. The fluid interface is parameterized isothermally. The traveling wave ansatz for parameterized surfaces is described. Waves are computed using Fourier collocation and quasi-Newton iteration; large amplitude overturned traveling waves are computed via a dimension-breaking based numerical continuation method.

Computing hyperbolic choreographies

An algorithm is presented for numerical computation of choreographies in spaces of constant negative curvature in a hyperbolic cotangent potential, extending the ideas given in a companion paper for computing choreographies in the plane in a Newtonian potential and on a sphere in a cotangent potential. Following an idea of Diacu, P\'{e}rez-Chavela and Reyes Victoria, we use stereographic projection and study the problem in the Poincar\'{e} disk. Using approximation by trigonometric polynomials and optimization methods with exact gradient and exact Hessian matrix, we find new choreographies, hyperbolic analogues of the ones presented in the companion paper. The algorithm proceeds in two phases: first BFGS quasi-Newton iteration to get close to a solution, then Newton iteration for high accuracy.

SAR Image Despeckling by the Use of Variational Methods With Adaptive Nonlocal Functionals

In this paper, we focus on the despeckling of synthetic aperture radar (SAR) images by variational methods which introduce nonlocal regularization functionals. To achieve this goal, two models are investigated from different aspects. The first model is derived for the logarithmically transformed (homomorphic) domain of the SAR data, and the other is derived for the original (nonhomomorphic) domain. The statistical properties of the speckle and the log-transformed speckle are analyzed, and the similarity measurements between pixels in the homomorphic domain and nonhomomorphic domain are then derived for constructing the corresponding nonlocal regularization functionals. Meanwhile, in the proposed models, we develop a strategy to adaptively choose the regularization parameters based on both the local heterogeneity information and the noise level of the images, aiming at getting a better balance between the goodness of fit of the original data and the amount of smoothing. A quasi-Newton iteration method is employed to quickly minimize the proposed adaptive nonlocal functionals. Experiments conducted on both simulated images and real SAR images confirm the good performances of the proposed methods, both in reducing speckle and preserving image quality.

The steady flying of a plasmonic flying head over a photoresist-coated surface in a near-field photolithography system

The near-field photolithography technique (NFPT) offers a new approach of nanolithography for a dramatic increase in the resolution with high throughput and low cost. The NFPT utilizes the same flight principle as that of the magnetic head of hard-disk drives but replacing the magnetic head with a plasmonic flying head. The plasmonic flying head, which can focus the incident laser beam to a spot size of sub-20 nm with an enhanced field intensity by exciting surface plasmon polaritons, takes off and then flies steadily above the revolving disk coated by a photoresist film to be patterned with a narrow gap of tens of nanometers. As a key foundation of the NFPT, the take off and flight stability of the plasmonic flying head affects the pattern density and the fabrication efficiency. This work proposed and investigated a molecular glass photoresist, named FPT-8Boc, for the large-scale consistent fabrication with the NFPT. To overcome the take-off problem of the head over the soft photoresist film, a transition zone is intentionally formed by washing off the coated photoresist in the outer area of the disk using a solvent. The simulation results by COMSOL Multiphysics software and quasi-Newton iteration method review that the matched transition zone height with spreading length can guarantee the flight stability of the plasmonic flying head on the soft photoresist. Using this method, a preliminary photolithography result with a 31 nm line width has been achieved.