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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. ..."
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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.
Splitting Methods for Dry Frictional Contact Problems in Rigid Multibody Systems: Preliminary Performance Results
"... A splitting method for solving LCP based models of dry frictional contact problems in rigid multibody systems based on box MLCP solver is presented. Since such methods rely on fast and robust box MLCP solvers, several methods are reviewed and their performance is compared both on random problems and ..."
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A splitting method for solving LCP based models of dry frictional contact problems in rigid multibody systems based on box MLCP solver is presented. Since such methods rely on fast and robust box MLCP solvers, several methods are reviewed and their performance is compared both on random problems and on simulation data. We provide data illustrating the convergence rate of the splitting method which demonstrates that they present a viable alternative to currently available methods.
Basis and Tripartition Identification for Quadratic Programming and Linear Complementarity Problems  From an interior solution to an optimal basis and viceversa
, 1996
"... 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 simplexb ..."
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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 simplexbased 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 we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal...
Example 4.1
"... In this chapter we discuss several methods for solving the LCP based on principal pivot steps. One common feature of these methods is that they do not introduce any arti cial variable. These methods employ either single or double principal pivot steps, and are guaranteed to process LCPs associated w ..."
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In this chapter we discuss several methods for solving the LCP based on principal pivot steps. One common feature of these methods is that they do not introduce any arti cial variable. These methods employ either single or double principal pivot steps, and are guaranteed to process LCPs associated with Pmatrices or PSDmatrices or both. We consider the LCP (q � M) oforder n, which is the following in tabular form. w z q I;M q w � z> 0 � w T z =0 (4:1)
ON TIGHT MONOMIALS IN QUANTIZED ENVELOPING ALGEBRAS
"... Abstract. In this paper, the author studies when some monomials are in the canonical basis of the quantized enveloping algebra corresponding to a simply laced semisimple finite dimensional complex Lie algebra. To any graph Γ, Lusztig has associated in [L1] and [L2] an algebra U − over Z[v, v−1] prov ..."
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Abstract. In this paper, the author studies when some monomials are in the canonical basis of the quantized enveloping algebra corresponding to a simply laced semisimple finite dimensional complex Lie algebra. To any graph Γ, Lusztig has associated in [L1] and [L2] an algebra U − over Z[v, v−1] provided with a canonical basis B. In the case that Γ is the Dynkin graph of a simply laced semisimple finite dimensional complex Lie algebra g, thenU−is the negative part of the corresponding quantized enveloping algebra U and B, the
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 Ma ..."
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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.