A dual approach to solving linear inequalities by unconstrained quadratic optimization.
Popescu, Elena (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Popescu, Elena (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Alain Billionnet, Sourour Elloumi, Marie-Christine Plateau (2008)
RAIRO - Operations Research
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Many combinatorial optimization problems can be formulated as the minimization of a 0–1 quadratic function subject to linear constraints. In this paper, we are interested in the exact solution of this problem through a two-phase general scheme. The first phase consists in reformulating the initial problem either into a compact mixed integer linear program or into a 0–1 quadratic convex program. The second phase simply consists in submitting the reformulated problem to a standard solver....
Wang, Xianyun (2009)
Journal of Inequalities and Applications [electronic only]
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I. Czochralska (1982)
Applicationes Mathematicae
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Matthias Knobloch (2004)
Kybernetika
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We consider general convex large-scale optimization problems in finite dimensions. Under usual assumptions concerning the structure of the constraint functions, the considered problems are suitable for decomposition approaches. Lagrangian-dual problems are formulated and solved by applying a well-known cutting-plane method of level-type. The proposed method is capable to handle infinite function values. Therefore it is no longer necessary to demand the feasible set with respect to the...
Mustafa Ç. Pinar, Marc Teboulle (2006)
RAIRO - Operations Research
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We consider the non-convex quadratic maximization problem subject to the unit ball constraint. The nature of the norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, derive SDP-like relaxations and raise open questions.
Ritu Narang, S.R. Arora (2009)
The Yugoslav Journal of Operations Research
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