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Some Generalizations Of The CrissCross Method For Quadratic Programming
 MATH. OPER. UND STAT. SER. OPTIMIZATION
, 1992
"... Three generalizations of the crisscross method for quadratic programming are presented here. Tucker's, Cottle's and Dantzig's principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program. A finite criss ..."
Abstract

Cited by 13 (8 self)
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Three generalizations of the crisscross method for quadratic programming are presented here. Tucker's, Cottle's and Dantzig's principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program. A finite crisscross method, based on leastindex resolution, is constructed for solving the LCP. In proving finiteness, orthogonality properties of pivot tableaus and positive semidefiniteness of quadratic matrices are used. In the last section some special cases and two further variants of the quadratic crisscross method are discussed. If the matrix of the LCP has full rank, then a surprisingly simple algorithm follows, which coincides with Murty's `Bard type schema' in the P matrix case.
Solving the Inverse Problem for Measures Using Iterated Function Systems: A New Approach
 Adv. Appl. Prob
, 1995
"... We present a systematic method of approximating, to an arbitrary accuracy, a probability measure ¯ on [0; 1] q ; q 1, with invariant measures for Iterated Function Systems by matching its moments. There are two novel features in our treatment: (1) An infinite number of fixed affine contraction ma ..."
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Cited by 12 (6 self)
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We present a systematic method of approximating, to an arbitrary accuracy, a probability measure ¯ on [0; 1] q ; q 1, with invariant measures for Iterated Function Systems by matching its moments. There are two novel features in our treatment: (1) An infinite number of fixed affine contraction maps on X; W = fw 1 ; w 2 ; : : :g, subject to an "fflcontractivity" condition, is employed. Thus, only an optimization over the associated probabilities p i is required. (2) We prove a Collage Theorem for Moments which reduces the moment matching problem to that of minimizing the "collage distance" between moment vectors. The minimization procedure is a standard quadratic programming problem in the p i which can be solved in a finite number of steps. Some numerical calculations for the approximation of measures on [0,1] are presented. AMS Subject Classifications: 28A, 41A, 58F 1. Introduction This paper is concerned with the approximation of probability measures on a compact metric space X ...
Edmonds Fukuda Rule And A General Recursion For Quadratic Programming
"... A general framework of nite algorithms is presented here for quadratic programming. This algorithm is a direct generalization of Van der Heyden's algorithm for the linear complementarity problem and Jensen's `relaxed recursive algorithm', which was proposed for solution of Oriented Matroid programmi ..."
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A general framework of nite algorithms is presented here for quadratic programming. This algorithm is a direct generalization of Van der Heyden's algorithm for the linear complementarity problem and Jensen's `relaxed recursive algorithm', which was proposed for solution of Oriented Matroid programming problems. The validity of this algorithm is proved the same way as the finiteness of the crisscross method is proved. The second part of this paper contains a generalization of EdmondsFukuda pivoting rule for quadratic programming. This generalization can be considered as a finite version of Van de Panne  Whinston algorithm and so it is a simplex method for quadratic programming. These algorithms uses general combinatorial type ideas, so the same methods can be applied for oriented matroids as well. The generalization of these methods for oriented matroids is a subject of another paper.