ABSTRACT
This chapter presents a general quadratic programming algorithm. It is general in the sense that it leaves unspecified the method for solving the relevant linear equations. The model problem for this method has nonnegativity constraints and its updating relies on the assumption that many variables will be zero at intermediate iterations. The chapter provides the parametric extension of the general quadratic programming algorithm. It also provides updating formulae for a symmetric matrix. The update finds the inverse of the modified matrix when a row and column are added to the matrix. When a row and column are deleted from the matrix and when a row and column are exchanged. These updates are used to make the general quadratic programming algorithm and its parametric extension into implementable algorithms. The first two of these updates can be viewed as special cases of the Bordered Inverse Lemma. The third is obtained from the Sherman-Morrison-Woodbury formula.
