article · Operations Research Forum
A new nonlinear conjugate gradient method has been developed for solving unconstrained optimisation problems. The approach uses a three-term search direction alongside the strong Wolfe line search strategy to determine step length. Modifying an existing search direction from recent literature, this formulation satisfies the sufficient descent condition naturally, without requiring extra conditions or restrictions. Theoretical convergence has been established for smooth functions that possess Lipschitz continuous gradients. In numerical evaluations using a collection of standard benchmark test problems, the technique demonstrated competitive performance against established alternatives. Beyond standard test functions, the formulation has been applied directly to robotic arm motion control, showing its practical relevance for handling physical trajectory and control calculations.
Optimisation algorithms form the mathematical backbone of modern engineering and automated systems. By ensuring sufficient descent without cumbersome mathematical restrictions, this method improves calculation reliability. Demonstrating its use in robotic arm control indicates that theoretical algorithmic improvements can directly benefit physical automation, potentially leading to smoother and more reliable trajectory calculations in robotic systems.
The method directly targets motion control for robotic arms, indicating relevance for industrial automation, robotics software developers, and control systems engineers. Because the approach has been tested on standard benchmarks and applied to a robotic arm control problem, it sits at an applied research stage. Further development into software packages or embedded controllers would be required to assess its performance in real-time industrial deployment.
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This paper presents a new nonlinear conjugate gradient method in which the new search direction comprises three terms, and the step length is required to satisfy the well-known strong Wolfe line search strategy. The new three-term search direction is a modification of a recently published one in the literature. Unlike the search direction that was modified, the new search direction satisfies the important sufficient descent condition without imposing additional conditions or restrictions. We discuss the convergence results of the proposed method under the assumption that the function is smooth and its gradient is Lipschitz continuous. We present numerical experiments on a collection of benchmark test problems and compare the new method’s performance with some existing ones. Finally, we apply the method to robotic arm motion control.
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DOI: 10.1007/s43069-025-00493-2
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