Parametric Pivoting Algorithm for Parametric Quadratic Programming Problem

There are many applications related to parametric quadratic programming. The parametric quadratic programming problem causes much more computation than the common quadratic programming problem. We employ the parametric pivoting algorithm to improve the computing efficiency of the parametric quadratic programming problem. The algorithm can decrease calculation to obtain solution of quadratic programming problem by solving a small linear inequality system which is the linear part of the Karush-Kuhn-Tucker (KKT) conditions for the quadratic programming problem and is equivalent to the KKT conditions while maintaining complementarity conditions of the KKT conditions to hold. The key of the algorithm is the deduction of the parametric formula which can obtain the optimal solution of the problem under new value of the parameter more efficiently by making full use of the information of the obtained optimal solution to the problem under former value of the parameter. The parametric formula further decreases the computation of the optimal solutions under different value of parameter.