scholarly journals Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhifeng Dai
Keyword(s):  
Conjugate Gradient Method ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Equality Constraints ◽  
Gradient Projection ◽  
Gradient Projection Method ◽  
Linear Equality Constraints ◽  
Linear Equality

Combining the Rosen gradient projection method with the two-term Polak-Ribière-Polyak (PRP) conjugate gradient method, we propose a two-term Polak-Ribière-Polyak (PRP) conjugate gradient projection method for solving linear equality constraints optimization problems. The proposed method possesses some attractive properties: (1) search direction generated by the proposed method is a feasible descent direction; consequently the generated iterates are feasible points; (2) the sequences of function are decreasing. Under some mild conditions, we show that it is globally convergent with Armijio-type line search. Preliminary numerical results show that the proposed method is promising.

A New Conjugate Gradient Projection Method and its Application

2013 ◽  
Vol 756-759 ◽  
pp. 3537-3541
Author(s):  
Hong Fang Cui ◽  
Ting Zhou
Keyword(s):  
Linear Model ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Estimation Algorithm ◽  
Equality Constraints ◽  
Gradient Projection ◽  
Gradient Projection Method

This paper constructs a new P-DY conjugate gradient projection method, the parameter contains parameters, it can be good to adjust the parameters of, this method makes the problem much faster, and more accurate results can be obtained iteratively. The decline of this algorithm and search convergence principle under the condition of Wolfe line, and will test new estimation algorithm, it is applied to the linear model with equality constraints and the results show that the effect is very good.

scholarly journals On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Strong Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Line Searches ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense thatlim infk→∞∥∇f(xk)∥=0when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense thatlimk→∞∥∇f(xk)∥=0under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.

An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and its Applications to Mechanical Design

1993 ◽  
Author(s):  
B. K. Kannan ◽  
Steven N. Kramer
Keyword(s):  
Lagrange Multiplier ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Continuous Optimization ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Augmented Lagrange Multiplier

Abstract An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher & Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer / discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

scholarly journals A Penalized Linear and Nonlinear Combined Conjugate Gradient Method for the Reconstruction of Fluorescence Molecular Tomography

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Shang Shang ◽  
Jing Bai ◽  
Xiaolei Song ◽  
Hongkai Wang ◽  
Jaclyn Lau
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Reconstruction Algorithms ◽  
Fluorescence Molecular Tomography ◽  
Nonlinear Conjugate Gradient Method ◽  
Gradient Based ◽  
Linear And Nonlinear

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

scholarly journals A Modified Three-Term Type CD Conjugate Gradient Algorithm for Unconstrained Optimization Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhan Wang ◽  
Pengyuan Li ◽  
Xiangrong Li ◽  
Hongtruong Pham
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Trust Region ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
General Function ◽  
Term Type

Conjugate gradient methods are well-known methods which are widely applied in many practical fields. CD conjugate gradient method is one of the classical types. In this paper, a modified three-term type CD conjugate gradient algorithm is proposed. Some good features are presented as follows: (i) A modified three-term type CD conjugate gradient formula is presented. (ii) The given algorithm possesses sufficient descent property and trust region property. (iii) The algorithm has global convergence with the modified weak Wolfe–Powell (MWWP) line search technique and projection technique for general function. The new algorithm has made great progress in numerical experiments. It shows that the modified three-term type CD conjugate gradient method is more competitive than the classical CD conjugate gradient method.

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