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A New Bound for the Quadratic Assignment Problem Based on Convex Quadratic Programming
 MATHEMATICAL PROGRAMMING
, 1999
"... We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the wellknown projected eigenvalue bound, and appears to be comp ..."
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Cited by 31 (3 self)
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We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the wellknown projected eigenvalue bound, and appears to be competitive with existing bounds in the tradeoff between bound quality and computational effort.
Polynomiality of PrimalDual Affine Scaling Algorithms for Nonlinear Complementarity Problems
, 1995
"... This paper provides an analysis of the polynomiality of primaldual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu's scaled Lipschitz condition, but is also applicable to ..."
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Cited by 11 (4 self)
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This paper provides an analysis of the polynomiality of primaldual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu's scaled Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primaldual affine scaling algorithms generates an approximate solution (given a precision ffl) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial of n, ln(1=ffl) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in [13].
A Unifying Investigation of InteriorPoint Methods for Convex Programming
 FACULTY OF MATHEMATICS AND INFORMATICS, TU DELFT, NL2628 BL
, 1992
"... In the recent past a number of papers were written that present low complexity interiorpoint methods for different classes of convex programs. Goal of this article is to show that the logarithmic barrier function associated with these programs is selfconcordant, and that the analyses of interiorp ..."
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Cited by 5 (4 self)
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In the recent past a number of papers were written that present low complexity interiorpoint methods for different classes of convex programs. Goal of this article is to show that the logarithmic barrier function associated with these programs is selfconcordant, and that the analyses of interiorpoint methods for these programs can thus be reduced to the analysis of interiorpoint methods with selfconcordant barrier functions.
Complexity of some inverse shortest path lengths problems,” Networks
"... The input to an inverse shortest path lengths problem (ISPL) consists of a graph G with arc weights, and a collection of sourcesink pairs with prescribed distances that do not necessarily conform to the shortest path lengths in G. The goal is to modify the arc weights, subject to a penalty on the d ..."
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Cited by 1 (0 self)
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The input to an inverse shortest path lengths problem (ISPL) consists of a graph G with arc weights, and a collection of sourcesink pairs with prescribed distances that do not necessarily conform to the shortest path lengths in G. The goal is to modify the arc weights, subject to a penalty on the deviation from the given weights, so that the shortest path lengths are equal to the prescribed values. We show that although ISPL is an NPhard problem, several ISPL classes are polynomially solvable. These cases include ISPL where the collection of the pairs share a single source and all other nodes as destinations (the singlesource allsink problem SAISPL). For the case where the collection contains a single node pair (the singlesource singlesink problem SSISPL), we identify conditions on the uniformity of the penalty functions and on the original arc weights, which make SSISPL polynomially solvable. These results cannot be strengthened significantly as the general singlesource ISPL is NPhard and the allsink case, with more than one source, is also NPhard. We further provide a convex programming formulation for a relaxation of ISPL in which the shortest path lengths are only required to be no less than the given values (LBISPL). It is demonstrated how this compact formulation leads to efficient algorithms for ISPL.