Conjugate Gradient Projection Research Articles

An improved spectral conjugate gradient projection method for monotone nonlinear equations with application

An improved spectral conjugate gradient projection method for monotone nonlinear equations with application

Approaches for fast Brownian dynamics simulation with constraints

Constraints can be used to eliminate quickly fluctuating degrees of freedom in dynamical systems enabling solutions that resolve the behavior of the system with fewer time steps over long time scales. In Brownian dynamics models, these constraints lead to linear equations which represent saddle point problems describing the velocity tangent to the constraint manifold and the forces resulting from imposition of the constraint on the dynamics. Simulations of these constrained systems must solve these saddle point problems, which are often ill-conditioned and require clever preconditioning in order to facilitate large scale simulation using iterative methods like GMRES. In this work, we show that the projected conjugate gradient (PrCG) method, which applies conjugate gradients projected onto the tangent space of the constraint manifold, has certain advantages compared to preconditioned iterative methods like GMRES, without the need to devise and compute a preconditioner. Specifically, for simulations of beads interacting hydrodynamically with commonly encountered holonomic constraints, PrCG exhibits linear scaling with the number of beads similar to GMRES. However, because PrCG does not require a preconditioner it often requires less precomputational effort both in terms of computational complexity and storage, depending on the nature of the constraints. Furthermore, PrCG produces iterates which are always feasible, allowing for independent tuning of the error tolerance on the bead velocities from the error tolerance on the constraint equations. We demonstrate PrCG's efficiency by solving several example low Reynolds number systems involving rigid bodies, freely jointed chains, and immobile particles, as well as a mixed constraint problem with both a rigid body and immobile particles, comparing to GMRES and analytical solutions, when available.

A conjugate gradient projection method with restart procedure for solving constraint equations and image restorations

A conjugate gradient projection method with restart procedure for solving constraint equations and image restorations

An accelerated relaxed-inertial strategy based CGP algorithm with restart technique for constrained nonlinear pseudo-monotone equations to image de-blurring problems

In this paper, an accelerated spectral conjugate gradient projection algorithm is proposed for solving the constrained nonlinear pseudo-monotone equations. We set a restart procedure related to the conjugate parameter in the search direction of the spectral conjugate gradient method. We use an accelerated gradient descent scheme to generate the spectral parameter. Finally, we adopt the relaxed-inertial strategy to accelerated algorithm iteration process. Global convergence is proved under mild conditions without the Lipschitz continuity assumption. Numerical comparisons with other methods show the performances of our algorithm for solving large-scale equations. Our applications are on regularized decentralized logistic regression and image de-blurring problems.

An inertial spectral conjugate gradient projection method for constrained nonlinear pseudo-monotone equations

An inertial spectral conjugate gradient projection method for constrained nonlinear pseudo-monotone equations

A family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial extensions for the constrained nonlinear pseudo-monotone equations with applications

A family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial extensions for the constrained nonlinear pseudo-monotone equations with applications

A New Hybrid Conjugate Gradient Projection Method for Solving Nonlinear Monotone Equations

In this study, we propose a new modified hybrid conjugate gradient projection method with a new scale parameter φ k for solving large-scale nonlinear monotone equations. The proposed method includes two major features: projection techniques and sufficient descent property independent of line search technique. Global convergence of the proposed method is proved under some suitable assumptions. Finally, numerical results illustrating the robustness of the suggested strategy and its comparisons are shown.

Predictive control of microwave hot-air coupled drying model based on GWO-BP neural network

A GB-MPC control algorithm (GWO-BP-MPC) was proposed to solve the problem of precise temperature control of fruit and vegetable coupling drying devices. Firstly, the BP (Back Propagation) neural network was improved using the Grey Wolf Optimizer (GWO) algorithm to increase the relevance and accuracy of the prediction model. By means of an improved neural network, we developed a high-accuracy predictive model for temperature control of drying units. Secondly, the projection conjugate gradient method was proposed for nonlinear optimization of the control system to improve the solving speed and accuracy of the optimal solution. The GB-MPC control algorithm was compared with the PID controller. The experimental results shown that the convergence speed of GB-MPC control was faster, the time took to reach a steady state in a single stage was shortened by 47 seconds compared with PID control. In the control process, the temperature change range of the GB-MPC control algorithm was smaller and there was no overshoot problem, which gave a better control effect than PID.

A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing

A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing

GRAPH-THEORETICAL APPROACH TO ROBUST 3D NORMAL EXTRACTION OF LIDAR DATA

Abstract. Low dimensional primitive feature extraction from LiDAR point clouds (such as planes) forms the basis of majority of LiDAR data processing tasks. A major challenge in LiDAR data analysis arises from the irregular nature of LiDAR data that forces practitioners to either regularize the data using some form of gridding or utilize a triangular mesh such as triangulated irregular network (TIN). While there have been a handful applications using LiDAR data as a connected graph, a principled treatment of utilizing graph-theoretical approach for LiDAR data modelling is still lacking. In this paper, we try to bridge this gap by utilizing graphical approach for normal estimation from LiDAR point clouds. We formulate the normal estimation problem in an optimization framework, where we find the corresponding normal vector for each LiDAR point by utilizing its nearest neighbors and simultaneously enforcing a graph smoothness assumption based on point samples. This is a non-linear constrained convex optimization problem which can then be solved using projected conjugate gradient descent to yield an unique solution. As an enhancement to our optimization problem, we also provide different weighted solutions based on the dot product of the normals and Euclidean distance between the points. In order to assess the performance of our proposed normal extraction method and weighting strategies, we first provide a detailed analysis on repeated randomly generated datasets with four different noise levels and four different tuning parameters. Finally, we benchmark our proposed method against existing state-of-the-art approaches on a large scale synthetic plane extraction dataset. The code for the proposed approach along with the simulations and benchmarking is available at https://github.com/arpan-kusari/graph-plane-extraction-simulation.

A spectral conjugate gradient projection algorithm to solve the large-scale system of monotone nonlinear equations with application to compressed sensing

In this paper, a derivative-free spectral projection technique to solve a system of large-scale nonlinear monotone equations is presented. The primary motivation is to use the appropriate structure of spectral conjugate gradient directions in the projection algorithms. The new direction is derivative-free and requires a little storage and computation. So, it is an appropriate direction to use in large-scale projection algorithms. We prove the global convergence and R-linear convergence rate of the proposed algorithm under some suitable conditions. Numerical experiments show a promising behaviour of the proposed algorithm to deal with large-scale monotone equations. Additionally, as a practical application, we use the new method to solve the -norm regularization problems to reconstruct a sparse signal in compressed sensing.

A three-term CGPM-based algorithm without Lipschitz continuity for constrained nonlinear monotone equations with applications

In this work, a new three-term conjugate gradient projection method (CGPM) with a new adaptive line search strategy is proposed for solving the large-scale nonlinear monotone equations with convex constraints. The proposed three-term CGPM-based algorithm has the following characteristics: (i) its search direction satisfies the sufficient descent and trust region properties which is independent of the line search; (ii) the nonlinear equations only satisfy continuous and monotone properties; (iii) its global convergence is analyzed and obtained without the Lipschitz continuity. Some preliminary numerical experiment results are reported and their corresponding performance profiles are illustrated, which show that the proposed algorithm is effective. Finally, the proposed algorithm is extended to solve sparse signal restoration problems.

A modified PRP-type conjugate gradient projection algorithm for solving large-scale monotone nonlinear equations with convex constraint

Conjugate gradient methods stand out as the most ideal iterative algorithms for solving nonlinear system of equations with large-dimensions. This is due to the fact that they are implemented with less memory and because of their ability to converge globally to solutions of problems considered. One of the most essential iterative method in this category is the Polak–Ribière–Polyak (PRP) scheme, which is numerically effective, but its search directions are mostly not descent directions. In this paper, based upon the adaptive PRP scheme by Yuan et al. and the projection method, a numerically efficient PRP-type scheme for system of monotone nonlinear equations is presented, where the solution is restricted to a closed convex set. Apart from the ability to satisfy the condition that is quite vital for global convergence, a distinct novelty of the new scheme is its application in compressive sensing, where it is applied to restore blurry images. The scheme’s global convergence is established with mild assumptions. Preliminary numerical results show that the method proposed is promising.

First and second order unconditionally energy stable schemes for topology optimization based on phase field method

In this paper, we use the phase field method to deal with the compliance minimization problem in topology optimization. A modified Allen-Cahn type equation with two penalty terms is proposed. The equation couples the diffusive interface dynamics and the linear elasticity mechanics. We propose the first- and second-order unconditionally energy stable schemes for the evolution of phase field modeling. The linearly stabilized splitting scheme is applied to improve the stability. The Crank-Nicolson scheme is applied to achieve second-order accuracy in time. We prove the unconditional stabilities of our schemes in analysis. The finite element method and the projected conjugate gradient method combining with fast fourier transform are used to solve the compliance minimization problem. Several experimental results are presented to verify the efficiency and accuracy of the proposed schemes.

A derivative-free RMIL conjugate gradient projection method for convex constrained nonlinear monotone equations with applications in compressive sensing

In this paper, a derivative-free RMIL conjugate gradient projection method for solving large-scale nonlinear monotone equations with convex constraints is proposed. The proposed method is a modification of an RMIL conjugate gradient method combined with the projection techniques. We establish its global convergence under appropriate conditions. The method is then compared with other existing methods in the literature and the numerical results indicate that the method is efficient. Furthermore, the proposed method is used to recover a sparse signal from an incomplete and contaminated sampling measurements and the results are promising.

A generalized hybrid CGPM-based algorithm for solving large-scale convex constrained equations with applications to image restoration

In this paper, by improving a line search criterion to yield steplength, and designing a hybrid conjugate parameter to construct sufficient descent direction, we propose a generalized hybrid conjugate gradient projection method for solving large-scale monotone nonlinear equations with convex constraints. For the proposed method, we prove its global convergence under some mild conditions, and study its convergence rate. Numerical comparisons with two existing methods show that our method is promising for solving large-scale nonlinear constrained equations. Furthermore, the experiment results of dealing with image restoration problems also verify that the proposed method is effective.

A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications

In this paper, based on the three-term conjugate gradient method and the hybrid technique, we propose a hybrid three-term conjugate gradient projection method by incorporating the adaptive line search for solving large-scale nonlinear monotone equations with convex constraints. The search direction generated by the proposed method is close to the one yielded by the memoryless BFGS method, and has the sufficient descent property and the trust region property independent of line search technique. Under some mild conditions, we establish the global convergence of the proposed method. Our numerical experiments show the effectiveness and robustness of the proposed method in comparison with two existing algorithms in the literature. Moreover, we show applicability and encouraging efficiency of the proposed method by extending it to solve sparse signal restoration and image de-blurring problems.

Three-Term of New Conjugate Gradient Projection Approach under Wolfe Condition to Solve Unconstrained Optimization Problems

Three-Term of New Conjugate Gradient Projection Approach under Wolfe Condition to Solve Unconstrained Optimization Problems

A New Conjugate Gradient Projection Method for Convex Constrained Nonlinear Equations

The conjugate gradient projection method is one of the most effective methods for solving large-scale monotone nonlinear equations with convex constraints. In this paper, a new conjugate parameter is designed to generate the search direction, and an adaptive line search strategy is improved to yield the step size, and then, a new conjugate gradient projection method is proposed for large-scale monotone nonlinear equations with convex constraints. Under mild conditions, the proposed method is proved to be globally convergent. A large number of numerical experiments for the presented method and its comparisons are executed, which indicates that the presented method is very promising. Finally, the proposed method is applied to deal with the recovery of sparse signals.

Least-Square-Based Three-Term Conjugate Gradient Projection Method for ℓ1-Norm Problems with Application to Compressed Sensing

In this paper, we propose, analyze, and test an alternative method for solving the ℓ 1 -norm regularization problem for recovering sparse signals and blurred images in compressive sensing. The method is motivated by the recent proposed nonlinear conjugate gradient method of Tang, Li and Cui [Journal of Inequalities and Applications, 2020(1), 27] designed based on the least-squares technique. The proposed method aims to minimize a non-smooth minimization problem consisting of a least-squares data fitting term and an ℓ 1 -norm regularization term. The search directions generated by the proposed method are descent directions. In addition, under the monotonicity and Lipschitz continuity assumption, we establish the global convergence of the method. Preliminary numerical results are reported to show the efficiency of the proposed method in practical computation.