Numerical Algorithm 94LVI

This chapter presents and investigates a numerical algorithm (termed 94LVI algorithm) for solving the QP problem subject to linear equality and bound constraints. To do this, as the previous chapter shows, the constrained QP problem is first converted into the LVI, which is then converted into an equivalent piecewise-linear equation (PLE). After that, the resultant PLE is solved by the presented 94LVI algorithm. The optimal numerical solution to the QP problem is thus obtained. Furthermore, the theoretical proof of the global convergence of the 94LVI algorithm is presented. Moreover, the numerical comparison results between the 94LVI algorithm and the active-set algorithm are provided, which further demonstrate the efficacy and superiority of the presented 94LVI algorithm for solving the QP problem.

[1]  Yunong Zhang.  Towards Piecewise-Linear Primal Neural Networks for Optimization and Redundant Robotics , 2006, 2006 IEEE International Conference on Networking, Sensing and Control.

[2]  Zhang Yu-nong,et al.  An LVI-based Numerical Algorithm for Solving Quadratic Programming Problems , 2012 .

[3]  Li Jian.  A Projection and Contraction Method for Convex Quadratic Programming , 2001 .

[4]  Bin-Xin He.  Solving a class of linear projection equations , 1994 .

[5]  Jun Wang,et al.  A dual neural network for constrained joint torque optimization of kinematically redundant manipulators , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[6]  Peter Sincak,et al.  Machine Intelligence: Quo Vadis? , 2004 .

[7]  N. Grudinin.  Reactive power optimization using successive quadratic programming method , 1998 .

[8]  Yunong Zhang,et al.  O(N 2)-Operation Approximation of Covariance Matrix Inverse in Gaussian Process Regression Based on Quasi-Newton BFGS Method , 2007, Commun. Stat. Simul. Comput..

[9]  Bingsheng He,et al.  A new method for a class of linear variational inequalities , 1994, Math. Program..

[10]  Jun Wang,et al.  RECURRENT NEURAL NETWORKS FOR REAL-TIME COMPUTATION OF INVERSE KINEMATICS OF REDUNDANT MANIPULATORS , 2004 .

[11]  Jun Wang,et al.  Obstacle avoidance for kinematically redundant manipulators using a dual neural network , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[12]  Bingsheng He,et al.  A projection and contraction method for a class of linear complementarity problems and its application in convex quadratic programming , 1992 .

[13]  Yunong Zhang.  On the LVI-based primal-dual neural network for solving online linear and quadratic programming problems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[14]  R. Fletcher.  A General Quadratic Programming Algorithm , 1971 .

[15]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[16]  Lei Zhang,et al.  Bi-criteria Velocity Minimization of Robot Manipulators Using a Linear Variational Inequalities-Based Primal-Dual Neural Network and PUMA560 Example , 2008, Adv. Robotics.

[17]  M. J. D. Powell,et al.  A method for nonlinear constraints in minimization problems , 1969 .

[18]  Tor Arne Johansen,et al.  Constrained nonlinear control allocation with singularity avoidance using sequential quadratic programming , 2004, IEEE Transactions on Control Systems Technology.