## Iterative Linear Programming for Linear Complementarity and Related Problems |

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### Contents

SOLVABILITY BY A SINGLE LINEAR PROGRAM | 8 |

Chapter HI THE ITERATIVE LINEAR PROGRAMMING METHOD | 21 |

THE SORBASED ILP METHOD | 57 |

2 other sections not shown

### Common terms and phrases

accumulation point algorithm assume assumption basis bounded Chapter characterization components computational convex combination convex programming cost vector current BFS d>0 satisfying defined denoted dominant matrix equality holds exists Exit at Step feasible point finite number Finite Termination follows Given xk global minimum Hence III.l implies index set induction hypothesis irreducible ITERATIVE LINEAR PROGRAMMING KKT point LCP M,q Lemke's method Lemma Let xk linear complementarity problem Mangasarian Mx+q nonnegative Note number of iterations number of pivots orthogonal SOR permutation matrix point of QP positive number positive semi positive semi-definite primal simplex method principal minors Proof quadratic program reordering the indices rithm satisfying III.3 set of M,q simplex based ILP simplex method solu solution of M,q solution set solvable solve the LCP solving linearly constrained SOR iteration SOR method SOR-based sparse matrix Theorem Let thesis tion unique solution University of Wisconsin-Madison vertex solution Z-matrix zero