Accelerated multiple step-size methods for solving unconstrained optimization problems

Ivanov, Branislav; Stanimirović, Predrag S.; Milovanović, Gradimir V.; Djordjević, Snežana; Brajević, Ivona

doi:10.1080/10556788.2019.1653868

Cited by 13 publications

(13 citation statements)

References 29 publications

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“…g k , (10) were defned in [19]. Furthermore, the next modifed SM (MSM) scheme was proposed in [21], using the output α k of the backtracking Algorithm 1 and the gain parameter ℷ k : � 1 + α k − α 2 k > 1 in the form of iterates.…”

Section: Introduction and Overview Of Related Resultsmentioning

confidence: 99%

A Modified Dai–Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application

Ivanov

Milovanović

Stanimirović

et al. 2023

Journal of Mathematics

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We introduce and investigate proper accelerations of the Dai–Liao (DL) conjugate gradient (CG) family of iterations for solving large-scale unconstrained optimization problems. The improvements are based on appropriate modifications of the CG update parameter in DL conjugate gradient methods. The leading idea is to combine search directions in accelerated gradient descent methods, defined based on the Hessian approximation by an appropriate diagonal matrix in quasi-Newton methods, with search directions in DL-type CG methods. The global convergence of the modified Dai–Liao conjugate gradient method has been proved on the set of uniformly convex functions. The efficiency and robustness of the newly presented methods are confirmed in comparison with similar methods, analyzing numerical results concerning the CPU time, a number of function evaluations, and the number of iterative steps. The proposed method is successfully applied to deal with an optimization problem arising in 2D robotic motion control.

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Section: Introduction and Overview Of Related Resultsmentioning

confidence: 99%

A Modified Dai–Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application

Ivanov

Milovanović

Stanimirović

et al. 2023

Journal of Mathematics

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“…The main goal of this research is to study the impact of multiple usage of backtracking line search in modified SM method [7] and practical computational performance of two new methods. Our intention is to propose and investigate improvements of the MSM method.…”

Section: Methods Acceleration Parameter γ K+1mentioning

confidence: 99%

“…A few variants of the IGD class (1.6) were proposed in [7,10,11,14,15]. The SM method belongs to the class IGD methods.…”

Section: Introductionmentioning

confidence: 99%

Multiple Use of Backtracking Line Search in Unconstrained Optimization

Ivanov¹,

Shaini

Stanimirović³

2021

FU Math Inform

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The gradient method is a very efficient iterative technique for solving unconstrained optimization problems. Motivated by recent modifications of some variants of the SM method, this study proposed two methods that are globally convergent as well as computationally efficient. Each of the methods is globally convergent under the influence of a backtracking line search. Results obtained from the numerical implementation of these methods and performance profiling show that the methods are very competitive with well-known traditional methods.

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“…The following modification of the SM method was defined in (Ivanov et al, 2021) as the transformation 𝑀𝑆𝑀 = ℳ(𝑆𝑀) defined by…”

Section: Problem Statementmentioning

confidence: 99%

Neutrosophy in Unconstrained Nonlinear Optimization

Stanimirović¹

2023

European Proceedings of Computers and Technology

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Determining the step length in iterations of nonlinear minimization represents a problem that is not uniquely defined. Motivated by such uncertainty in defining step length, our intention was to use the capabilities of neutrosophy in this process. Our idea is to unify the usability and numerous applications of neutrosophic logic and the enormous importance of nonlinear optimization. An improvement of line search iteration for solving unconstrained optimization is proposed using appropriately defined Neutrosophic logic system in determining appropriate step size for the class of descent direction methods. The basic idea is to use an additional parameter that would monitor the behavior of the objective function and, based on that, correct the step length in known optimization methods. Mutual comparison and analysis of generated numerical results reveal better results generated by the suggested iterations compared to analogous available iterations considering the statistical ranking technique. Statistical measures show advantages of fuzzy improvements of considered line search optimization methods.

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Accelerated multiple step-size methods for solving unconstrained optimization problems

Cited by 13 publications

References 29 publications

A Modified Dai–Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application

A Modified Dai–Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application

Multiple Use of Backtracking Line Search in Unconstrained Optimization

Neutrosophy in Unconstrained Nonlinear Optimization

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