A sufficient descent conjugate gradient method and its global convergence

Cheng, Yunlong; Qiong, Mou; Pan, Xianbing; Yao, Shengwei

doi:10.1080/10556788.2015.1124431

Cited by 11 publications

(11 citation statements)

References 19 publications

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“…One direction was to find the best fixed value for t and the other the best approximation for t in each iteration. Analyzing the results from [18,26,131,139], we conclude that the scalar t was defined by a fixed value of 0.1 in numerical experiments. Also, numerical experience related to the fixed valued t = 1 was reported in [26].…”

Section: Dai-liao Methods and Its Variants An Extension Of The Conjugmentioning

confidence: 85%

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A survey of gradient methods for solving nonlinear optimization

Stanimirović¹,

Mathematics²,

Ivanov³

et al. 2020

era

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<p style='text-indent:20px;'>The paper surveys, classifies and investigates theoretically and numerically main classes of line search methods for unconstrained optimization. Quasi-Newton (QN) and conjugate gradient (CG) methods are considered as representative classes of effective numerical methods for solving large-scale unconstrained optimization problems. In this paper, we investigate, classify and compare main QN and CG methods to present a global overview of scientific advances in this field. Some of the most recent trends in this field are presented. A number of numerical experiments is performed with the aim to give an experimental and natural answer regarding the numerical one another comparison of different QN and CG methods.</p>

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Section: Dai-liao Methods and Its Variants An Extension Of The Conjugmentioning

confidence: 85%

“…, µ 3 ∈ (0, +∞) and 1 is an any given positive constant. Motivated by these modifications, in [29] the authors defined the modified PRP method as [18] gave a variant of the PRP method which we call the WYL method, that is,…”

Section: Denominatormentioning

confidence: 99%

A survey of gradient methods for solving nonlinear optimization

Stanimirović¹,

Mathematics²,

Ivanov³

et al. 2020

era

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“…wherein t > 0 is a scalar. Some well-known formulas for defining β k have been created by modifying the conjugate gradient parameter β DL k [2][3][4][5][6][7][8][9]. One of them is denoted as β MHSDL k and defined in [7] by…”

Section: Introduction and Background Resultsmentioning

confidence: 99%

“…So far, the research in finding the appropriate value of t has evolved in two directions. One group of methods is aimed at finding an appropriate fixed value for t [1,2,[6][7][8], while methods from another group promote appropriate rules for computing values of t in each iteration, which ensure a satisfactory decrease of the objective. In our research, we will pay attention to the second research stream: find the parameter t whose values change through iterations so that the faster convergence is achieved.…”

Section: Introduction and Background Resultsmentioning

confidence: 99%

A Novel Value for the Parameter in the Dai-Liao-Type Conjugate Gradient Method

Ivanov

Stanimirović

Shaini

et al. 2021

Journal of Function Spaces

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A new rule for calculating the parameter t involved in each iteration of the MHSDL (Dai-Liao) conjugate gradient (CG) method is presented. The new value of the parameter initiates a more efficient and robust variant of the Dai-Liao algorithm. Under proper conditions, theoretical analysis reveals that the proposed method in conjunction with backtracking line search is of global convergence. Numerical experiments are also presented, which confirm the influence of the new value of the parameter t on the behavior of the underlying CG optimization method. Numerical comparisons and the analysis of obtained results considering Dolan and Moré’s performance profile show better performances of the novel method with respect to all three analyzed characteristics: number of iterative steps, number of function evaluations, and CPU time.

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“…However, this approach was restricted to parameter identification problems. e common nonlinear least squares iterative solutions [21] are the gradient descent method [22], Gauss-Newton method [23], and Levenberg-Marquart (LM) method [24,25]. For example, in [26], the nonlinear least squares problem of the distributional robust parameter identification model for time-delay systems is transformed into a single-level optimization problem and a gradient-based optimization method is developed to solve the transformed problem.…”

Section: Introductionmentioning

confidence: 99%

Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem

et al. 2020

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In this work, we combine the special structure of the separable nonlinear least squares problem with a variable projection algorithm based on singular value decomposition to separate linear and nonlinear parameters. en, we propose finding the nonlinear parameters using the Levenberg-Marquart (LM) algorithm and either solve the linear parameters using the least squares method directly or by using an iteration method that corrects the characteristic values based on the L-curve, according to whether or not the nonlinear function coefficient matrix is ill posed. To prove the feasibility of the proposed method, we compared its performance on three examples with that of the LM method without parameter separation. e results show that (1) the parameter separation method reduces the number of iterations and improves computational efficiency by reducing the parameter dimensions and (2) when the coefficient matrix of the linear parameters is well-posed, using the least squares method to solve the fitting problem provides the highest fitting accuracy. When the coefficient matrix is ill posed, the method of correcting characteristic values based on the L-curve provides the most accurate solution to the fitting problem.

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A sufficient descent conjugate gradient method and its global convergence

Cited by 11 publications

References 19 publications

A survey of gradient methods for solving nonlinear optimization

A survey of gradient methods for solving nonlinear optimization

A Novel Value for the Parameter in the Dai-Liao-Type Conjugate Gradient Method

Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem

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