Suliman Al-Homidan

Data completion techniques offer numerous advantages in various fields. However, completing large datasets that must satisfy specific criteria can be challenging, necessitating the use of approximative completion methods. The primary objective of this research paper is to showcase the substantial influence of the initial point selection on the completed matrix, emphasizing the distinctiveness of solutions corresponding to each initial point. However, in the case of using the same initial point, a unique solution is attainable although the employed completion methods may exhibit variations. Each method utilized for the completion of Hankel positive semidefinite matrices strives to achieve a unique solution, assuming feasibility. Nevertheless, the path to reaching this solution can differ among methods due to variations in the number of iterations and accuracy measures required for convergence. The paper will extensively explore theoretical aspects, algorithmic advancements, and empirical findings related to completing Hankel matrices through semidefinite programming (SDP) and combining SDP with second‐order cone optimization (SOCP). The study will present numerical results to support the analyses conducted.

Purpose: The purpose of this paper is to introduce a spectral conjugate gradient method specifically designed to solve unconstrained optimization problems, particularly concerning the motion control of a two-joint planar robotic manipulator.Design/methodology/approach: Our approach integrates a spectral parameter derived from the strong Wolfe line search with the conjugate gradient method of Dai and Kou. This approach is evaluated through computational simulations, demonstrating its effectiveness in motion control scenarios. Our design and methodology underscore a rigorous analytical framework combined with practical, application-oriented testing to validate the proposed algorithm’s efficiency and applicability in robotic motion control.Findings: We were able to find an effective way to select the spectral parameter, which is crucial for the optimization process in robotic motion control. This improved selection process directly contributes to enhanced numerical performance. Moreover, the implementation of the proposed method in motion control of a two-joint planar robotic manipulator demonstrates its effectiveness. This suggests that the approach not only works theoretically but also proves to be viable in practical, real-world applications. Furthermore, the findings indicate that this approach could potentially be adapted or extended to other types of robotic systems or motion control challenges.Originality/value: This paper introduces an enhancement to the spectral conjugate gradient method, marked by a clever parameter selection strategy originating from the strong Wolfe line search, tailored specifically for robotic motion control.