A quadratic simplex algorithm for primal optimization over zero-one polytopes
A primal quadratic simplex algorithm tailored to the optimization over the vertices of a polytope is presented. Starting from a feasible vertex, it performs either strictly improving or admissible non-deteriorating steps in order to determine a locally optimum basic feasible solution in terms of the...
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| Vydáno v: | Discrete Applied Mathematics Ročník 347; s. 285 - 296 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
15.04.2024
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| ISSN: | 0166-218X, 1872-6771 |
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| Abstract | A primal quadratic simplex algorithm tailored to the optimization over the vertices of a polytope is presented. Starting from a feasible vertex, it performs either strictly improving or admissible non-deteriorating steps in order to determine a locally optimum basic feasible solution in terms of the quadratic objective function. The algorithm so generalizes over local improvement methods for according applications, including in particular quadratic optimization problems whose feasible solutions correspond to vertices of a 0-1 polytope. Computational experiments for unconstrained binary quadratic programs, maximum cut, and the quadratic assignment problem serve as a proof of concept and underline the importance of a pivoting rule that is able to accept at least a restricted class of degenerate steps. |
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| AbstractList | A primal quadratic simplex algorithm tailored to the optimization over the vertices of a polytope is presented. Starting from a feasible vertex, it performs either strictly improving or admissible non-deteriorating steps in order to determine a locally optimum basic feasible solution in terms of the quadratic objective function. The algorithm so generalizes over local improvement methods for according applications, including in particular quadratic optimization problems whose feasible solutions correspond to vertices of a 0-1 polytope. Computational experiments for unconstrained binary quadratic programs, maximum cut, and the quadratic assignment problem serve as a proof of concept and underline the importance of a pivoting rule that is able to accept at least a restricted class of degenerate steps. |
| Author | Mallach, Sven |
| Author_xml | – sequence: 1 givenname: Sven surname: Mallach fullname: Mallach, Sven email: smallach@cs.uni-bonn.de organization: High Performance Computing & Analytics Lab, University of Bonn, Friedrich-Hirzebruch Allee 8, 53115 Bonn, Germany |
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| Cites_doi | 10.1016/0024-3795(79)90018-1 10.1137/0110022 10.1023/A:1019758821507 10.1287/mnsc.17.11.698 10.1007/BF01580136 10.1287/moor.2.2.103 10.1016/0167-6377(92)90043-3 10.1016/S0167-8191(05)80147-4 10.1007/s10107-003-0384-8 10.1137/S1052623400382467 10.1023/A:1017912624016 10.2307/1909468 10.1007/s12532-014-0075-x 10.1093/imanum/11.3.299 10.1137/0120019 10.1137/0220004 10.1002/nav.3800060305 10.1287/ijoc.2017.0798 10.1016/0167-6377(88)90049-1 10.1145/227683.227684 10.1287/mnsc.44.3.336 10.2307/3007121 10.1287/opre.11.2.248 10.1287/mnsc.9.4.586 10.1007/s10107-008-0235-8 |
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| Title | A quadratic simplex algorithm for primal optimization over zero-one polytopes |
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