Results 1 
9 of
9
A Superlinearly Convergent Infeasibleinteriorpoint Algorithm for Degenerate LCP
 DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF IOWA, IOWA CITY, IA
, 1995
"... A largestep infeasible pathfollowing method is proposed for solving general linear complementarity problems with sufficient matrices. If the problem has a solution the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. The algorithm generates poi ..."
Abstract

Cited by 17 (11 self)
 Add to MetaCart
A largestep infeasible pathfollowing method is proposed for solving general linear complementarity problems with sufficient matrices. If the problem has a solution the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. The algorithm generates
A superlinearly convergent predictorcorrector method for degenerate LCP in a wide neighborhood of the central path with O (√n L)iteration complexity
, 2006
"... ..."
Local Convergence of InteriorPoint Algorithms for Degenerate Monotone LCP
 Computational Optimization and Applications
, 1993
"... Most asymptotic convergence analysis of interiorpoint algorithms for monotone linear complementarity problems assumes that the problem is nondegenerate, that is, the solution set contains a strictly complementary solution. We investigate the behavior of these algorithms when this assumption is remo ..."
Abstract

Cited by 38 (5 self)
 Add to MetaCart
is removed. 1 Introduction In the monotone linear complementarity problem (LCP), we seek a vector pair (x; y) 2 IR n \Theta IR n that satisfies the conditions y = Mx+ q; x 0; y 0; x T y = 0; (1) where q 2 IR n , and M 2 IR n\Thetan is positive semidefinite. We use S to denote the solution set
A Path Following Method for LCP with Superlinearly Convergent Iteration Sequence
 Department of Mathematics, The University of Iowa, Iowa City, IA
, 1995
"... A new algorithm for solving linear complementarity problems with sufficient matrices is proposed. If the problem has a solution the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. Each iteration requires only one matrix factorization and at most ..."
Abstract

Cited by 10 (9 self)
 Add to MetaCart
A new algorithm for solving linear complementarity problems with sufficient matrices is proposed. If the problem has a solution the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. Each iteration requires only one matrix factorization
PREPRINTMCSP3570493,MATHEMATICSANDCOMPUTERSCIENCEDIVISION,ARGONNENATIONALLABORATORY LocalConvergenceofInteriorPointAlgorithmsfor RenatoD.C.MonteiroandStephenWrighty DegenerateMonotoneLCP April6,1993 1Introduction thesolutionsetcontainsastrictlycompleme
"... thisauthorwasbasedonresearchsupportedbytheNationalScienceFoundationundergrantDDM9109404 SystemsandIndustrialEngineeringDepartment,UniversityofArizona,Tucson,AZ85721.Theworkof J=fi=1;;njxi=yi=0forall(x;y)2Sg: (2) andtheOceofNavalResearchundergrantN000149310234. Argonne,IL60439.Theworkofthisauthor ..."
Abstract
 Add to MetaCart
thisauthorwasbasedonresearchsupportedbytheNationalScienceFoundationundergrantDDM9109404 SystemsandIndustrialEngineeringDepartment,UniversityofArizona,Tucson,AZ85721.Theworkof J=fi=1;;njxi=yi=0forall(x;y)2Sg: (2) andtheOceofNavalResearchundergrantN000149310234. Argonne,IL60439.TheworkofthisauthorwasbasedonresearchsupportedbytheOceofScientic Computing,U.S.DepartmentofEnergy,underContractW31109Eng38. yMathematicsandComputerScienceDivision,ArgonneNationalLaboratory,9700SouthCassAvenue, 1Lemma1.1Thereisan(x;y)2Ssuchthatxi>0foralli2Bandyi>0forall i2N. thepropertythatxi>0fori2Bandyi>0fori2N.Dene Proof.ChoosejBj+jNjmembers(xi;yi)ofS(wherejjdenotessetcardinality)with checkthaty=Mx+qand(x)Ty=0.Moreover,xi>0foralli2Bandyi>0forall Since(xi)Tyj=(xj)Tyi=0foranytwosolutions(xi;yi)and(xj;yj)of(1),itiseasyto i2N,givingtheresult. Aninfeasibleinteriorpointalgorithmsolves(1)bygeneratingasequenceofstrictlypos Assumption1canberestatedsimplyasJ=;. (x;y)=1 jBj+jNjX i2B[N(xi;yi): presentation,\Qsuperlinearconvergence"alwaysmeansQsuperlinearconvergenceofthe in(1)inthelimitask!1.Feasibleinteriorpointalgorithmsrequirealliteratestosatisfy yk=Mxk+qinadditiontostrictpositivity(xk;yk)>0. itiveiteratesf(xk;yk)g,k=0;1;2;,whileaimingtosatisfythetwoequalityrelationships
su + xv = ɛxs − u v
"... Erratum: A superlinearly convergent predictorcorrector method for degenerate LCP in a wide neighborhood of the central path with O ( √ nL)iteration complexity Received: date / Revised version: date Abstract. We correct an error in Algorithm 2 from [1] Key words. linear complementarity problem, int ..."
Abstract
 Add to MetaCart
Erratum: A superlinearly convergent predictorcorrector method for degenerate LCP in a wide neighborhood of the central path with O ( √ nL)iteration complexity Received: date / Revised version: date Abstract. We correct an error in Algorithm 2 from [1] Key words. linear complementarity problem
A Complementary Pivoting Approach to the Maximum Weight Clique Problem
 SIAM J. OPTIM
, 2002
"... Given an undirected graph with positive weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having largest total weight. The problem is known to be NPhard, even to approximate. Motivated by a recent quadratic program ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
complementarity. Despite this regularity result, however, the LCP turns out to be inherently degenerate, and we find that Lemke’s wellknown pivoting method, equipped with standard degeneracy resolution strategies, yields unsatisfactory experimental results. We exploit the degeneracy inherent in the problem
On Characterization of Quadratic Splines
, 2002
"... A quadratic spline is a di#erentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature, and al ..."
Abstract
 Add to MetaCart
that the representation can be refined in a neighborhood of a nondegenerate point and a set of nondegenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship
Abstract Magnetoacoustic rotation of transverse waves in 3 HeB
, 1999
"... In superfluid 3 HeB, the offresonant coupling of the J = 2 − , M = ±1 order parameter collective modes to transverse current excitations stabilizes propagating transverse waves with low damping for frequencies above that of the J = 2 − modes. Right (RCP) and left circularly polarized (LCP) transv ..."
Abstract
 Add to MetaCart
In superfluid 3 HeB, the offresonant coupling of the J = 2 − , M = ±1 order parameter collective modes to transverse current excitations stabilizes propagating transverse waves with low damping for frequencies above that of the J = 2 − modes. Right (RCP) and left circularly polarized (LCP