Semidefinite programming for discrete optimization and matrix completion problems
Henry Wolkowicz,Miguel F. Anjos +1 more
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TL;DR: A recipe for finding SDP relaxations based on adding redundant constraints and using Lagrangian relaxation is presented and a new application of SDP to find approximate matrix completions for large and sparse instances of Euclidean distance matrices is concluded.
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About: This article is published in Discrete Applied Mathematics. The article was published on 15 Nov 2002. and is currently open access. The article focuses on the topics: Semidefinite programming & Matrix completion.
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Citations
A semidefinite optimization approach for the single-row layout problem with unequal dimensions
TL;DR: A semidefinite programming (SDP) relaxation is constructed providing a lower bound on the optimal value of the one-dimensional space-allocation problem (ODSAP), also known as the single-row facility layout problem, which consists in finding an optimal linear placement of facilities with varying dimensions on a straight line.
159
Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes
Miguel F. Anjos,Anthony Vannelli +1 more
TL;DR: It is demonstrated that the combination of a semidefinite programming relaxation with cutting planes is able to compute globally optimal layouts for large SRFLPs with up to 30 facilities.
Global registration of multiple point clouds using semidefinite programming
TL;DR: In this paper, the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP), by setting up connections between the uniqueness of this SDP and results fr...
A convex optimisation framework for the unequal-areas facility layout problem
TL;DR: Computational results showing that the proposed framework consistently produces competitive, and often improved, layouts for well-known large instances when compared with other approaches in the literature are presented.
52
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LP approximations to mixed-integer polynomial optimization problems
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TL;DR: An approximation scheme for the "AC-OPF" problem on graphs with bounded tree-width is obtained and a more general construction for pure binary optimization problems where individual constraints are available through a membership oracle is described.
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