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dc.contributor.authorFrangioni, Antonio
dc.contributor.authorFurini, Fabio
dc.contributor.authorGentile, Claudio
dc.date.accessioned2017-03-16T12:19:30Z
dc.date.available2017-03-16T12:19:30Z
dc.date.issued2016
dc.identifier.issn0926-6003
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16373
dc.language.isoenen
dc.subjectMixed-integer nonlinear problemsen
dc.subjectSemi-continuous variablesen
dc.subjectPerspective reformulationen
dc.subjectProjectionen
dc.subject.ddc515en
dc.subject.classificationjelC25en
dc.titleApproximated perspective relaxations: a project and lift approachen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe perspective reformulation (PR) of a Mixed-Integer NonLinear Program with semi-continuous variables is obtained by replacing each term in the (separable) objective function with its convex envelope. Solving the corresponding continuous relaxation requires appropriate techniques. Under some rather restrictive assumptions, the Projected PR (P2R) can be defined where the integer variables are eliminated by projecting the solution set onto the space of the continuous variables only. This approach produces a simple piecewise-convex problem with the same structure as the original one; however, this prevents the use of general-purpose solvers, in that some variables are then only implicitly represented in the formulation. We show how to construct an Approximated Projected PR (AP2R) whereby the projected formulation is “lifted” back to the original variable space, with each integer variable expressing one piece of the obtained piecewise-convex function. In some cases, this produces a reformulation of the original problem with exactly the same size and structure as the standard continuous relaxation, but providing substantially improved bounds. In the process we also substantially extend the approach beyond the original P2R development by relaxing the requirement that the objective function be quadratic and the left endpoint of the domain of the variables be non-negative. While the AP2R bound can be weaker than that of the PR, this approach can be applied in many more cases and allows direct use of off-the-shelf MINLP software; this is shown to be competitive with previously proposed approaches in some applications.en
dc.relation.isversionofjnlnameComputational Optimization and Applications
dc.relation.isversionofjnlvol63en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2016-04
dc.relation.isversionofjnlpages705-735en
dc.relation.isversionofdoi10.1007/s10589-015-9787-8en
dc.relation.isversionofjnlpublisherKluwer Academic Publishersen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2017-03-16T12:09:25Z
hal.person.labIds17464
hal.person.labIds989
hal.person.labIds232408
hal.identifierhal-01491122*


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