arXiv subjects

Qing-Na Li

Publications and source records attributed to Qing-Na Li.

3 recordsLinked to original sources

arXiv2025

Triangle Steepest Descent: A Geometry-Based Gradient Algorithm with Guaranteed R-Linear Convergence

Gradient methods are among the simplest yet most widely used algorithms for unconstrained optimization. Motivated by a geometric property of the steepest descent (SD) method that can alleviate the zigzag behavior in quadratic problems, we develop a new gradient variant called the Triangle Steepest Descent (TSD) method. The TSD method introduces a cycle parameter $j$ that governs the periodic combination of past search directions, providing a geometry-driven mechanism to enhance convergence. To the best of our knowledge, TSD is the first formally established geometry-based gradient scheme since Akaike (1959). We prove that TSD is at least R-linearly convergent for strongly convex quadratic problems and demonstrate through extensive numerical experiments that it exhibits superlinear behavior, outperforming the Barzilai-Borwein (BB) method and monotone Dai-Yuan gradient method (DY) in quadratic cases. These results suggest that incorporating geometric information into gradient directions offers a promising avenue for developing efficient optimization algorithms.

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arXiv2021

An Efficient Quadratic Programming Relaxation Based Algorithm for Large-Scale MIMO Detection

Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in the fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance, and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient sparse quadratic programming (SQP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as an SQP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the SQP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power method.

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arXiv2020

A Novel Posture Positioning Method for Multi-Joint Manipulators

Safety and automatic control are extremely important when operating manipulators. For large engineering manipulators, the main challenge is to accurately recognize the posture of all arm segments. In classical sensing methods, the accuracy of an inclinometer is easily affected by the elastic deformation in the manipulator's arms. This results in big error accumulations when sensing the angle of joints between arms one by one. In addition, the sensing method based on machine vision is not suitable for such kind of outdoor working situation yet. In this paper, we propose a novel posture positioning method for multi-joint manipulators based on wireless sensor network localization. The posture sensing problem is formulated as a Nearest-Euclidean-Distance-Matrix (NEDM) model. The resulting approach is referred to as EDM-based posture positioning approach (EPP) and it satisfies the following guiding principles: (i) The posture of each arm segment on a multi-joint manipulator must be estimated as accurately as possible; (ii) The approach must be computationally fast; (iii) The designed approach should not be susceptible to obstructions. To further improve accuracy, we explore the inherent structure of manipulators, i.e., fixed-arm length. This is naturally presented as linear constraints in the NEDM model. For concrete pumps, a typical multi-joint manipulator, the mechanical property that all arm segments always lie in a 2D plane is used for dimension-reduction operation. Simulation and experimental results show that the proposed method provides efficient solutions for posture sensing problem and can obtain preferable localization performance with faster speed than applying the existing localization methods.

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