Hybrid Modification of Accelerated Double Direction Method

Petrović, Milena J.; Stanimirović, Predrag S.; Kontrec, Nataša; Mladenović, Julija

doi:10.1155/2018/1523267

Cited by 12 publications

(7 citation statements)

References 12 publications

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“…Finally, let us emphasize that contemporary papers often use the Picard-Mann-Ishikawa iterative processes and they make the connection of these kinds of processes with the unconstrained optimization (see [29,37,38]).…”

Section: Resultsmentioning

confidence: 99%

Unconstrained Optimization Methods: Conjugate Gradient Methods and Trust-Region Methods

Djordjević¹

2019

Applied Mathematics

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Here, we consider two important classes of unconstrained optimization methods: conjugate gradient methods and trust region methods. These two classes of methods are very interesting; it seems that they are never out of date. First, we consider conjugate gradient methods. We also illustrate the practical behavior of some conjugate gradient methods. Then, we study trust region methods. Considering these two classes of methods, we analyze some recent results.

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Section: Resultsmentioning

confidence: 99%

Unconstrained Optimization Methods: Conjugate Gradient Methods and Trust-Region Methods

Djordjević¹

2019

Applied Mathematics

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“…There are many well-known conjugate gradient methods, such as [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][34][35][36][37][38][39][40][41][42]. In [12], the iterative formula of three-term conjugate gradient method is…”

Section: New Three-term Conjugate Gradient Methods For Smooth Casementioning

confidence: 99%

“…For three-term conjugate gradient methods [12][13][14][15][16][17][18][19][20][21][22] and the related methods [23][24][25][26] posse low memory requirement and simple implementation, conjugate gradient methods are often used for solving unconstrained optimization problems. Recently, many researchers have presented kinds of three-term conjugate gradient method for solving the unconstrained optimization problems.Hence, we consider using three-term conjugate gradient method to solve the finite minimax problems.…”

Section: Introductionmentioning

confidence: 99%

A new three-term conjugate gradient method for solving the finite minimax problems

Hao

Chen

2021

Filomat

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In this paper, we consider the method for solving the finite minimax problems. By using the exponential penalty function to smooth the finite minimax problems, a new three-term nonlinear conjugate gradient method is proposed for solving the finite minimax problems, which generates sufficient descent direction at each iteration. Under standard assumptions, the global convergence of the proposed new three-term nonlinear conjugate gradient method with Armijo-type line search is established. Numerical results are given to illustrate that the proposed method can efficiently solve several kinds of optimization problems, including the finite minimax problem, the finite minimax problem with tensor structure, the constrained optimization problem and the constrained optimization problem with tensor structure.

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“…A modified HSM (MHSM) method is defined in [92] by proposing an appropriate initial value in the backtracking procedure. A hybridization of the ADD method was considered in [99] in the form…”

Section: Gradient Methods Accelerated By Picard-mann Hybrid Iterativementioning

confidence: 99%

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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Hybrid Modification of Accelerated Double Direction Method

Cited by 12 publications

References 12 publications

Unconstrained Optimization Methods: Conjugate Gradient Methods and Trust-Region Methods

Unconstrained Optimization Methods: Conjugate Gradient Methods and Trust-Region Methods

A new three-term conjugate gradient method for solving the finite minimax problems

A survey of gradient methods for solving nonlinear optimization

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