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A semidefinite programming based polyhedral cut and price approach for the maxcut problem
 COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
, 2006
"... We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the wellknown SDP relaxation of maxcut is formulated as a semiinfinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this co ..."
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Cited by 16 (6 self)
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We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the wellknown SDP relaxation of maxcut is formulated as a semiinfinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this constitutes the pricing (column generation) phase of the algorithm. Cutting planes based on the polyhedral theory of the maxcut problem are then added to the primal problem in order to improve the SDP relaxation; this is the cutting phase of the algorithm. We provide computational results, and compare these results with a standard SDP cutting plane scheme.
Strong Duality and Minimal Representations for Cone Optimization
, 2008
"... The elegant results for strong duality and strict complementarity for linear programming, LP, can fail for cone programming over nonpolyhedral cones. One can have: unattained optimal values; nonzero duality gaps; and no primaldual optimal pair that satisfies strict complementarity. This failure is ..."
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Cited by 14 (2 self)
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The elegant results for strong duality and strict complementarity for linear programming, LP, can fail for cone programming over nonpolyhedral cones. One can have: unattained optimal values; nonzero duality gaps; and no primaldual optimal pair that satisfies strict complementarity. This failure is tied to the nonclosure of sums of nonpolyhedral closed cones. We take a fresh look at known and new results for duality, optimality, constraint qualifications, and strict complementarity, for linear cone optimization problems in finite dimensions. These results include: weakest and universal constraint qualifications, CQs; duality and characterizations of optimality that hold without any CQ; geometry of nice and devious cones; the geometric relationships between zero duality gaps, strict complementarity, and the facial structure of cones; and, the connection between theory and empirical evidence for lack of a CQand failure of strict complementarity. One theme is the notion of minimal representation of the cone and the constraints in order to regularize the problem and avoid both the theoretical and numerical difficulties that arise due to (near) loss of a CQ. We include a discussion on obtaining these representations efficiently.
A conic interior point decomposition approach for large scale semidefinite programming
, 2005
"... ..."
Global lower bounds for the VLSI macrocell floorplanning problem using semidefinite optimization
 In Proceedings of IWSOC 2005
, 2005
"... We investigate the application of Semidefinite Programming (SDP) techniques to the VLSI macrocell floorplanning problem. We propose a new mixedinteger SDP formulation of the problem which leads to new SDP relaxations. This approach has been implemented and we report global lower bounds for some MCNC ..."
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Cited by 3 (1 self)
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We investigate the application of Semidefinite Programming (SDP) techniques to the VLSI macrocell floorplanning problem. We propose a new mixedinteger SDP formulation of the problem which leads to new SDP relaxations. This approach has been implemented and we report global lower bounds for some MCNC benchmark macrocell problems. 1
large scale semidefinite
, 2005
"... conic interior point decomposition approach for ..."
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Mathematical Programming manuscript No.
"... A conic interior point decomposition approach for semidefinite programming ..."
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A conic interior point decomposition approach for semidefinite programming