Basis- and partition identification for quadratic programming and linear complementarity problems

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximal complementary solutions. Maximal complementary solutions can be characterized by optimal (tri)partitions. On the other hand, the solutions provided by simplex{based pivot algorithms are given in terms of complementary bases. A basis identi cation algorithm is an algorithm which generates a complementary basis, starting from any complementary solution. A tripartition identi cation algorithm is an algorithmwhich generates a maximal complementary solution (and its corresponding tripartition), starting from any complementary solution. In linear programming such algorithms were respectively proposed by Megiddo in 1991 and Balinski and Tucker in 1969. In this paper we will present identi cation algorithms for quadratic programming and linear complementarity problems with su cient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus.