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任意初始点的广义投影算法 总被引:2,自引:0,他引:2
对于包含非线性等式与不等式的非线性优化问题,引入了可微的辅助函数,在初始点任意的情况下,采用广义投影算法,在合理假设下得到算法的整体收敛性。 相似文献
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目的 针对偏置冗余机械臂的逆运动学,采用传统数值法存在依赖初始值、奇异位姿收敛性差等问题,提出一种改进数值法。方法 首先将非线性方程组转化为同伦方程组,引入同伦延拓算法能够有效避免依赖初始值的问题,同时能够获取逆运动学解空间。然后考虑奇异位姿,将同伦方程组转化为最小二乘问题,采用Levenberg Marquardt算法对同伦方程组进行路径追踪,以获取逆运动学解空间。最后将关节极限避免问题映射为解空间优化问题,引入二进制改进粒子群优化算法,获得最优逆运动学解。结果 实验结果表明,相较于传统数值法,文中所提数值法针对逆运动学求解具有更高的收敛率、更快的收敛速度,同时二进制改进粒子群算法能够有效避免关节极限问题。结论 采用文中所提数值法求解逆运动学的精度较高,能够满足实时性要求,对于机械臂用于包装作业具有一定的理论意义和工程应用价值。 相似文献
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本文延拓辅助原理的技巧,来研究一类广义集值强非线性混合似变分不等式。首先,利用Ky Fan引理,证明了这类混合似变分不等式的辅助问题解的存存性。其次,利用该存在性结果,给出了解这类混合似变分不等式的迭代算法。最后。既证明了这类混合似变分不等式解的存在性,又证明了由算法生成的迭代序列的收敛性。 相似文献
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利用投影矩阵,对求解无约束规划的共轭梯度算法中的参数βk给一限制条件确定βk的取值范围,以保证得到目标函数的共轭梯度投影下降方向,建立了求解非线性等式约束优化问题的共轭梯度投影算法,并证明了算法的收敛性。数值例子表明算法是有效的。 相似文献
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本文对一类广义非线性集值混合拟变分不等式进行了研究.首先,利用刘理蔚与李育强的结果,可知黄南京的结果中出现的集值映像实际上是单值的.其次,利用Siddiqi和Ansari的方法以及不动点理论,我们证明了这类混合拟变分不等式解的存在性,并给出了一个解这类混合拟变分不等式的新的扰动迭代算法.最后,讨论了这个新的扰动迭代算法的收敛判据. 相似文献
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In this article, a superlinearly convergent trust region–sequential quadratic programming approach is first proposed, developed and investigated for nonlinear systems based on nonlinear model predictive control. The method incorporates a combination algorithm that allows both the trust region technique and the sequential quadratic programming method to be used. If the attempted search of the trust region method is not accepted, the line search rule will be adopted for the next iteration. Also, having to resolve the quadratic programming subproblem for nonlinear constrained optimization problems is avoided. This gives the potential for fast convergence in the neighbourhood of an optimal solution. Moreover, additional characteristics of the algorithm are that each quadratic programming subproblem is regularized and the quadratic programming subproblem always has a consistent point. The main result is illustrated on a nonlinear system with a variable parameter and a bipedal walking robot system through simulations and is utilized to achieve rapidly stability. Numerical results show that the trust region–sequential quadratic programming algorithm is feasible and effective for a nonlinear system with a variable parameter and a bipedal walking robot system. Therefore, the simulation results demonstrate the usefulness of the trust region–sequential quadratic programming approach with nonlinear model predictive control for real-time control systems. 相似文献
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基于半光滑性和Jacobi相容性,提出了求解非线性互补问题的一个光滑信赖域算法,并在一定条件下证明了该算法的全局收敛性和局部超线性收敛性。 相似文献
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J. A. Teixeira de Freitas David Lloyd Smith 《International journal for numerical methods in engineering》1984,20(11):2077-2092
The nonlinear system of equations and inequalities relating to the large displacement behaviour of elasto-plastic structures can be transformed by the method of perturbations into an infinite sequence of recursive linear complementarity problems (LCP). Each such LCP can be solved by a simple variant of the simplex algorithm of linear programming. Special consideration is given to describing those steps of the algorithm that are needed for detecting and controlling the phenomena of plastic straining, unstressing and branching. 相似文献
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研究一类非线性时滞双曲型偏泛函微分方程解的振动性,利用微分不等式方法和广义Riccati变换,获得了该类方程在第一类边值条件下振动的新的充分条件,所得结果通过实例加以阐明. 相似文献