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Updated: Sep 18, 2025

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An efficient gradient-based algorithm with descent direction for unconstrained optimization with applications to

Sulaiman Mohammed Ibrahim1,2, Aliyu M Awwal3, Maulana Malik4

  • 1School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Kedah, Malaysia.

Peerj. Computer Science
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Summary
This summary is machine-generated.

A new gradient algorithm improves optimization models for image restoration and robotic control. This modified conjugate gradient method ensures stability and demonstrates superior performance in experiments.

Keywords:
Convergence analysisGradient based methodImage restorationRobotic motion controlUnconstrained optimization

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Area of Science:

  • Optimization Algorithms
  • Computer Science Applications
  • Applied Mathematics

Background:

  • Optimization models are crucial for complex tasks like image restoration and robotic control.
  • Existing gradient-based methods face challenges in maintaining descent properties and ensuring global convergence.
  • The conjugate gradient (CG) method is a widely used optimization technique.

Purpose of the Study:

  • To introduce a novel gradient-based algorithm enhancing optimization model performance.
  • To ensure the modified conjugate gradient (CG) coefficient maintains the search direction's descent property.
  • To establish the global convergence of the proposed algorithm under specific conditions.

Main Methods:

  • Development of a modified conjugate gradient (CG) algorithm.
  • Ensuring the CG coefficient (β κ) integration into the search direction.
  • Utilizing strong Wolfe conditions and assuming Lipschitz continuity for convergence analysis.

Main Results:

  • The algorithm maintains the descent property under appropriate line search conditions.
  • Global convergence of the proposed algorithm is theoretically established.
  • Computational experiments show superior performance in image restoration and robotic motion control (3DOF arm).

Conclusions:

  • The novel gradient-based algorithm offers enhanced performance for optimization models.
  • The method shows significant potential for practical applications in image processing and robotics.
  • The established global convergence provides a strong theoretical foundation for the algorithm's reliability.