Numerical Algorithm E47

In this chapter, based on the linear variational inequality (LVI), a numerical algorithm (termed E47 algorithm), which won the ICAL2011 best paper award (Zhang et al. in Proceedings of IEEE International Conference on Automation and Logistics, pp. 125–130, 2011), is presented and investigated to solve the QP problem that is simultaneously subject to linear equality, inequality, and bound constraints. Note that the constrained QP problem can be converted to a linear variational inequality and then to a piecewise-linear equation (PLE). The E47 algorithm is then adapted to solving the resultant PLE, and thus the optimal numerical solution to the QP problem is obtained. In addition, the global linear convergence of such an E47 algorithm is proved. The numerical comparison results between such an E47 algorithm and the active-set algorithm are further provided. The efficacy and superiority of the presented E47 algorithm for QP solving are substantiated.

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