METHODS FOR QUADRATIC-PROGRAMMING - A SURVEY

A survey is presented of methods for solving the general quadratic programming problem. The discussion is centered on (i) the unification of several classes of finite methods, (ii) recent developments of iterative methods and (iii) the numerical implementation of several finite and iterative methods for large scale applications. A major objective of the present paper is to give a unified treatment to many of the best-known finite methods. More specifically, the authors attempt to derive these methods from a basic pivoting algorithm due to Keller and to differentiate them according to their numerical implementation procedures. Another objective of the paper is to give a general iterative scheme for solving a linear complementarity problem and to explain how the scheme can be specialized to obtain iterative methods for solving strictly convex quadratic programs. Some convergence results will also be stated.