Two numerical algorithms and numerical experiments for efficiently solving inequality-and-bound constrained QP

Abstract

This paper presents and investigates two new numerical algorithms (i.e., E47 algorithm and 94LVI algorithm) for solving the quadratic programming (QP) problem subject to inequality and bound constraints. Such a constrained QP problem is firstly converted equivalently into a linear variational inequality (LVI), and then converted equivalently into a piecewise-linear projection equation (PLPE). The E47 and 94LVI algorithms are employed to solve the resultant PLPE, and thus the optimal numerical solution to the QP problem is obtained readily. In this paper, we analyze the computational complexities and present the global convergence of the E47 and 94LVI algorithms. Moreover, the numerical-experiment results of E47 and 94LVI algorithms (compared with those of the active set algorithm) illustrate the efficacy and superiority of the presented algorithms for solving such inequality-and-bound constrained QP problems. Such two numerical algorithms can thus be applied safely and successfully to the motion planning and control of redundant robot manipulators, e.g., a real redundant robot manipulator, PA10 and PUMA560 robot manipulators, as well as wheeled mobile manipulators.