Basis- and Tripartition Identification for Quadratic Programming and LinearComplementarity Problems from an Interior Solution to an Optimal Basis and Viceversa

摘要

Optimal solutions of interior point algorithms for linear and quadraticprogramming 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 identification algorithm is an algorithm which generates a complementary basis, starting from any complementary solution. A tripartition identification algorithm is an algorithm which 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 the authors will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus. (Copyright (c) 1996 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)