The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrai...The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes- sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.展开更多
In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path ...In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective func- tion nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.展开更多
针对RRT*(rapidly-exploring random tree star)算法在复杂障碍物场景下存在收敛效率低、搜索方向随机性强,导致生成路径效果不佳的问题,提出一种基于动态梯度采样和人工势场的双向快速探索随机树算法(SN-BIRRT*)。采用分步式动态梯度...针对RRT*(rapidly-exploring random tree star)算法在复杂障碍物场景下存在收敛效率低、搜索方向随机性强,导致生成路径效果不佳的问题,提出一种基于动态梯度采样和人工势场的双向快速探索随机树算法(SN-BIRRT*)。采用分步式动态梯度采样策略优化采样过程,更有效地探索配置空间。在拓展方面引入一种改进的人工势场法,提高算法的收敛速度。对生成的新节点采用改进的重连父节点策略进行优化,减少路径总成本。为了提高路径的平滑度,采用路径剪枝、线性插值和B样条平滑的融合路径平滑策略进行后处理。通过仿真实验,将SN-BIRRT*算法与其他几种基于采样的路径规划算法在不同障碍物环境和狭窄环境下进行了比较,结果表明该算法在不同环境下均有良好的性能,在机器人路径规划中可以有效解决机器人在复杂室内环境中的高效路径规划问题。展开更多
基金the National Natural Science Foundation of China under Grant No.10471094the Ph.D.Foundation under Grant No.0527003+1 种基金the Shanghai Leading Academic Discipline Project (T0401)the Science Foundation of Shanghai Education Committee under Grant No.05DZ11
文摘The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes- sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
基金the National Science Foundation of China Grant (10471094)the Ph.D.Foundation Grant (0527003) of Chinese Education Ministry+2 种基金the Shanghai Leading Academic Discipline Project (T0401)the Scientific Computing Key Laboratory of Shanghai Universitiesthe Science Foundation Grant (05DZ11) of Shanghai Education Committee
文摘In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective func- tion nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.
文摘针对RRT*(rapidly-exploring random tree star)算法在复杂障碍物场景下存在收敛效率低、搜索方向随机性强,导致生成路径效果不佳的问题,提出一种基于动态梯度采样和人工势场的双向快速探索随机树算法(SN-BIRRT*)。采用分步式动态梯度采样策略优化采样过程,更有效地探索配置空间。在拓展方面引入一种改进的人工势场法,提高算法的收敛速度。对生成的新节点采用改进的重连父节点策略进行优化,减少路径总成本。为了提高路径的平滑度,采用路径剪枝、线性插值和B样条平滑的融合路径平滑策略进行后处理。通过仿真实验,将SN-BIRRT*算法与其他几种基于采样的路径规划算法在不同障碍物环境和狭窄环境下进行了比较,结果表明该算法在不同环境下均有良好的性能,在机器人路径规划中可以有效解决机器人在复杂室内环境中的高效路径规划问题。
