This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on a...This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction.Under certain assumptions,the proposed method is proved to possess global convergence.Finally,our method is compared with other potential methods.A large number of numerical experiments show that our method is more competitive and effective.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugat...In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugate gradient methods with this formula is analyzed,and the corresponding results are as follows：（1） The DY method globally converges for a strongly convex LC^1 objective function;（2） The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, LC^1 objective function.展开更多
In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under...In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.展开更多
Microstrip transmission lines connecting to the millimeter wave radar chip and antenna significantly affect the radiation efficiency and bandwidth of the antenna.Here,a wideband non-uniform wavy microstrip line for co...Microstrip transmission lines connecting to the millimeter wave radar chip and antenna significantly affect the radiation efficiency and bandwidth of the antenna.Here,a wideband non-uniform wavy microstrip line for complex impedance in automotive radar frequency range is proposed.Unlike the gradient transmission line,the wavy structure is composed of periodically semi-circular segments.By adjusting the radius of the semi-circular,the surface current is varied and concentrated on the semi-circular segments,allowing a wider tunability range of the resonant frequency.The results reveal that the bandwidth of the loaded wavy transmission line antenna improves to 9.37 GHz,which is 5.81 GHz wider than that of the loaded gradient line.The gain and the half power beam width of the loaded antenna are about 14.69 dB and 9.58°,respectively.The proposed non-uniform microstrip line scheme may open up a route for realizing wideband millimeter-wave automotive radar applications.展开更多
In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmo...In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.展开更多
针对基于点线特征的实时定位与建图(simultaneous localization and mapping,SLAM)算法在位姿识别过程中对定位精度的要求,提出一种改进单目视觉惯性同步定位与建图(monocular visual-inertial SLAM with efficient point-line flow fea...针对基于点线特征的实时定位与建图(simultaneous localization and mapping,SLAM)算法在位姿识别过程中对定位精度的要求,提出一种改进单目视觉惯性同步定位与建图(monocular visual-inertial SLAM with efficient point-line flow features,EPLF-VINS)算法。首先,分析了梯度阈值参数对line segment detection by edge drawing(EDLines)线段提取算法的影响;其次,在点特征正向光流追踪后采用逆向光流追踪剔除错误追踪点,提高光流追踪正确率;然后,在EPLF-VINS算法的线段提取处融合一种自适应调节算法,通过计算逆向光流追踪后的点特征光流追踪成功率实时地调节梯度阈值参数,从而实现根据环境的变化动态调整线段提取,更好地平衡计算成本与定位精度的效果;最后,基于Robot Operating System(ROS)平台分析了改进EPLF-VINS算法与对比算法在EuRoc和TUM-VI数据集上的轨迹精度与效率。研究结果表明,改进EPLF-VINS算法绘制的轨迹曲线更加贴合真实轨迹,在保证实时性的同时具有更高的定位精度。展开更多
This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Po...This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases展开更多
Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with conve...Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.展开更多
Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that...Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that in [3] and relaxed beta(k) to be negative with the objective function being convex. This paper allows beta(k) to be selected in a wider range than [5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.展开更多
A hybrid method of the Polak-Ribière-Polyak (PRP) method and the Wei-Yao-Liu (WYL) method is proposed for unconstrained optimization pro- blems, which possesses the following properties: i) This method inherits a...A hybrid method of the Polak-Ribière-Polyak (PRP) method and the Wei-Yao-Liu (WYL) method is proposed for unconstrained optimization pro- blems, which possesses the following properties: i) This method inherits an important property of the well known PRP method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening;ii) The scalar holds automatically;iii) The global convergence with some line search rule is established for nonconvex functions. Numerical results show that the method is effective for the test problems.展开更多
基金Supported by 2023 Inner Mongolia University of Finance and Economics,General Scientific Research for Universities directly under Inner Mon‐golia,China (NCYWT23026)2024 High-quality Research Achievements Cultivation Fund Project of Inner Mongolia University of Finance and Economics,China (GZCG2479)。
文摘This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction.Under certain assumptions,the proposed method is proved to possess global convergence.Finally,our method is compared with other potential methods.A large number of numerical experiments show that our method is more competitive and effective.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
基金Supported by the National Natural Science Foundation of China(Grant No.11761014)the Natural Science Foundation of Guangxi Zhuang Autonomous Region(Grant No.2017GXNSFAA198243)+2 种基金Guangxi Basic Ability Improvement Project for the Middle-Aged and Young Teachers of Colleges and Universities(Grant Nos.2017KY0068KY2016YB069)Guangxi Higher Education Undergraduate Course Teaching Reform Project(Grant No.2017JGB147)
文摘In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugate gradient methods with this formula is analyzed,and the corresponding results are as follows：（1） The DY method globally converges for a strongly convex LC^1 objective function;（2） The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, LC^1 objective function.
基金This work is supported by the National Natural Science Foundation of China
文摘In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.
基金Supported by the National Natural Science Foundation of China( 61974104)。
文摘Microstrip transmission lines connecting to the millimeter wave radar chip and antenna significantly affect the radiation efficiency and bandwidth of the antenna.Here,a wideband non-uniform wavy microstrip line for complex impedance in automotive radar frequency range is proposed.Unlike the gradient transmission line,the wavy structure is composed of periodically semi-circular segments.By adjusting the radius of the semi-circular,the surface current is varied and concentrated on the semi-circular segments,allowing a wider tunability range of the resonant frequency.The results reveal that the bandwidth of the loaded wavy transmission line antenna improves to 9.37 GHz,which is 5.81 GHz wider than that of the loaded gradient line.The gain and the half power beam width of the loaded antenna are about 14.69 dB and 9.58°,respectively.The proposed non-uniform microstrip line scheme may open up a route for realizing wideband millimeter-wave automotive radar applications.
文摘In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.
文摘针对基于点线特征的实时定位与建图(simultaneous localization and mapping,SLAM)算法在位姿识别过程中对定位精度的要求,提出一种改进单目视觉惯性同步定位与建图(monocular visual-inertial SLAM with efficient point-line flow features,EPLF-VINS)算法。首先,分析了梯度阈值参数对line segment detection by edge drawing(EDLines)线段提取算法的影响;其次,在点特征正向光流追踪后采用逆向光流追踪剔除错误追踪点,提高光流追踪正确率;然后,在EPLF-VINS算法的线段提取处融合一种自适应调节算法,通过计算逆向光流追踪后的点特征光流追踪成功率实时地调节梯度阈值参数,从而实现根据环境的变化动态调整线段提取,更好地平衡计算成本与定位精度的效果;最后,基于Robot Operating System(ROS)平台分析了改进EPLF-VINS算法与对比算法在EuRoc和TUM-VI数据集上的轨迹精度与效率。研究结果表明,改进EPLF-VINS算法绘制的轨迹曲线更加贴合真实轨迹,在保证实时性的同时具有更高的定位精度。
基金Supported by the National Natural Science Foundation of China(1 0 1 6 1 0 0 2 ) and Guangxi Natural Sci-ence Foundation (0 1 3 5 0 0 4 )
文摘This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases
基金Supported by the National Natural Science Foundation of China (10871130)the Ph.D.Foundation of China Education Ministry (0527003)+1 种基金Shanghai Educational Development Foundationthe Science Foundation of Shanghai Education Committee(06A110)
文摘Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
文摘Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that in [3] and relaxed beta(k) to be negative with the objective function being convex. This paper allows beta(k) to be selected in a wider range than [5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.
文摘A hybrid method of the Polak-Ribière-Polyak (PRP) method and the Wei-Yao-Liu (WYL) method is proposed for unconstrained optimization pro- blems, which possesses the following properties: i) This method inherits an important property of the well known PRP method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening;ii) The scalar holds automatically;iii) The global convergence with some line search rule is established for nonconvex functions. Numerical results show that the method is effective for the test problems.
