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  • 1
    Electronic Resource
    Electronic Resource
    Semidefinite Programs and Association Schemes (1999)
    Springer
    Computing 63 (1999), S. 331-340 
    Details
    ISSN: 1436-5057
    Keywords: Key words.Semidefinite programming, association scheme, maximum cut problem.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract. We consider semidefinite programs, where the matrices defining the problem all arise from some association scheme. We show that in this case the semidefinite program can be solved through an ordinary linear program. As an application, we consider the max-cut problem, where the underlying graph arises from an association scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s006070050038
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Book review (1995)
    Springer
    Mathematical methods of operations research 41 (1995), S. 56-56 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415064
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  • 3
    Electronic Resource
    Electronic Resource
    A recipe for semidefinite relaxation for (0,1)-quadratic programming (1995)
    Springer
    Journal of global optimization 7 (1995), S. 51-73 
    Details
    ISSN: 1573-2916
    Keywords: Quadratic boolean programming ; semidefinite programming ; bounds ; Lagrangian duality ; parametric programming ; trust region subproblems ; minmax eigenvalue problems ; quadratic assignment problem ; graph partitioning ; max-clique ; theta function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We review various relaxations of (0,1)-quadratic programming problems. These include semidefinite programs, parametric trust region problems and concave quadratic maximization. All relaxations that we consider lead to efficiently solvable problems. The main contributions of the paper are the following. Using Lagrangian duality, we prove equivalence of the relaxations in a unified and simple way. Some of these equivalences have been known previously, but our approach leads to short and transparent proofs. Moreover we extend the approach to the case of equality constrained problems by taking the squared linear constraints into the objective function. We show how this technique can be applied to the Quadratic Assignment Problem, the Graph Partition Problem and the Max-Clique Problem. Finally we show our relaxation to be best possible among all quadratic majorants with zero trace.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01100205
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    Paper (German National Licenses)
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