A modified three–term conjugate gradient method with sufficient descent property

A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.

High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

Subspace Minimization Conjugate Gradient Method Based on Cubic Regularization Model for Unconstrained Optimization

Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

GLOBAL CONVERGENCE OF THE GENERAL THREE TERM CONJUGATE GRADIENT METHODS WITH THE RELAXED STRONG WOLFE LINE SEARCH

The global convergence of the general three term conjugate gradient methods with the relaxed strong Wolfe line search is proved.

IMPROVED PRECONDITIONED CONJUGATE GRADIENT METHOD AND ITS APPLICATION IN F.E.A.FOR ENGINEERING

In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, ft is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.

A CLASSOF NONMONOTONE CONJUGATE GRADIENT METHODSFOR NONCONVEX FUNCTIONS

This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases

CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUTSUFFICIENT DECREASE CONDITION

Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that in [3] and relaxed beta(k) to be negative with the objective function being convex. This paper allows beta(k) to be selected in a wider range than [5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.

NUMERICAL STUDY ON THE FLOW AROUND A CIRCULAR CYLINDER WITH SURFACE SUCTION OR BLOWING USING VORTICITY-VELOCITY METHOD

A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme ( MILU-CG). The effects of surface suction or blowing' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen, can reduce the drag force significantly, too.

An Efficient Projected Gradient Method for Convex Constrained Monotone Equations with Applications in Compressive Sensing

In this paper, a modified Polak-Ribière-Polyak conjugate gradient projection method is proposed for solving large scale nonlinear convex constrained monotone equations based on the projection method of Solodov and Svaiter. The obtained method has low-complexity property and converges globally. Furthermore, this method has also been extended to solve the sparse signal reconstruction in compressive sensing. Numerical experiments illustrate the efficiency of the given method and show that such non-monotone method is suitable for some large scale problems.

MILU-CG METHOD AND THE NUMERICAL STUDY ON THE FLOW AROUND A ROTATINGCIRCULAR CYLINDER

A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.

A Descent Gradient Method and Its Global Convergence

Y Liu and C Storey(1992)proposed the famous LS conjugate gradient method which has good numerical results.However,the LS method has very weak convergence under the Wolfe-type line search.In this paper,we give a new descent gradient method based on the LS method.It can guarantee the sufficient descent property at each iteration and the global convergence under the strong Wolfe line search.Finally,we also present extensive preliminary numerical experiments to show the efficiency of the proposed method by comparing with the famous PRP^+method.

An Inexact Halley's Method

An inexact Halley＇s method-Halley-PCG（preconditioned conjugate gradient） method is proposed for solving the systems of linear equations for improved Halley method either by Cholesky factorization exactly or by preconditioned conjugate gradient method approximately. The convergence result is given and the efficiency of the method compared to the improved Halley＇s method is shown.

Accuracy and Efficiency: The Comparison of Different RPC Parameters Solving Methods

As a generalized sensor, the RPC model with its accuracy equally matches the physical sensor model. Moreover, the accurate positioning combining with the flexibility in application leads the RPC model to be the priority in photogrammetry processing. Generally, the RPC model is calculated through a control grid. Different RPC parameters solving methods and the operation efficiency all serve as variables in the accuracy of the model. In this paper, the ridge estimation iterative method, spectrum correction iteration, and conjugate gradient method are employed to solve RPC parameters;the accuracy and efficiency of three solving methods are analyzed and compared. The results show that ridge estimation iterative method and spectrum correction iteration have obvious advantages in accuracy. The ridge estimation iterative method has fewer iteration times and time con-sumption, and spectrum correction iteration has more stable precision.

基于改进神经网络PID算法的医用电子直线加速器温控系统研究

目的:探讨基于改进神经网络PID算法的医用电子直线加速器温控系统的实现。方法:针对医用电子直线加速器温度控制难题,提出了基于共轭梯度算法改进的BP神经网路PID控制算法,并在温度控制系统中进行了仿真。结果:该控制器能够实现较好控制效果。结论:利用共轭梯度算法改进的BP神经网路PID控制算法对医用电子直线加速器温度控制系统进行控制方法切实有效,简单可行。

OPTIMIZATION APPROACH FOR THE MONGE-AMPèRE EQUATION

In this paper, we introduce and study a method for the numerical solution of the elliptic Monge-Ampere equation with Dirichlet boundary conditions. We formulate the Monge-Ampere equation as an optimization problem. The latter involves a Poisson Problem which is solved by the finite element Galerkin method and the minimum is computed by the conjugate gradient algorithm. We also present some numerical experiments.

TESTING DIFFERENT CONJUGATE GRADIENT METHODS FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION

In this paper we test different conjugate gradient (CG) methods for solving large-scale unconstrained optimization problems. The methods are divided in two groups: the first group includes five basic CG methods and the second five hybrid CG methods. A collection of medium-scale and large-scale test problems are drawn from a standard code of test problems, CUTE. The conjugate gradient methods are ranked according to the numerical results. Some remarks are given.

A Modified Hestenes-Stiefel Conjugate Gradient Method and Its Convergence

It is well-known that the direction generated by Hestenes-Stiefel （HS） conjugate gradient method may not be a descent direction for the objective function. In this paper, we take a little modification to the HS method, then the generated direction always satisfies the sufficient descent condition. An advantage of the modified Hestenes-Stiefel （MHS） method is that the scalar βκHS. keeps nonnegative under the weak Wolfe-Powell line search. The global convergence result of the MHS method is established under some mild conditions. Preliminary numerical results show that the MHS method is a little more efficient than PRP and HS methods.

Global Convergence of a Modified PRP Conjugate Gradient Method

In this paper, a modified formula for βk^PRP is proposed for the conjugate gradient method of solving unconstrained optimization problems. The value of βk^PRP keeps nonnegative independent of the line search. Under mild conditions, the global convergence of modified PRP method with the strong Wolfe-Powell line search is established. Preliminary numerical results show that the modified method is efficient.