Piecewise-linear pathways to the optimal solution set in linear programming

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dc.citation.epage634en_US
dc.citation.issueNumber3en_US
dc.citation.spage619en_US
dc.citation.volumeNumber93en_US
dc.contributor.authorPınar, M. Ç.en_US
dc.date.accessioned2016-02-08T10:48:09Z
dc.date.available2016-02-08T10:48:09Z
dc.date.issued1997en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractThis paper takes a fresh look at the application of quadratic penalty functions to linear programming. Recently, Madsen et al. (Ref. 1) described a continuation algorithm for linear programming based on smoothing a dual l1-formulation of a linear program with unit bounds. The present paper is prompted by the observation that this is equivalent to applying a quadratic penalty function to the dual of a linear program in standard canonical form, in the sense that both approaches generate continuous, piecewise-linear paths leading to the optimal solution set. These paths lead to new characterizations of optimal solutions in linear programming. An important product of this analysis is a finite penalty algorithm for linear programming closely related to the least-norm algorithm of Mangasarian (Ref. 2) and to the continuation algorithm of Madsen et al. (Ref. 1). The algorithm is implemented, and promising numerical results are given.en_US
dc.identifier.doi10.1023/A:102265133en_US
dc.identifier.issn0022-3239
dc.identifier.urihttp://hdl.handle.net/11693/25627
dc.language.isoEnglishen_US
dc.publisherKluwer Academic Publishers - Plenum Publishersen_US
dc.relation.isversionofhttps://doi.org/10.1023/A:102265133en_US
dc.source.titleJournal of Optimization Theory and Applicationsen_US
dc.subjectCharacterization of optimal solutionsen_US
dc.subjectFinitenessen_US
dc.subjectLinear programmingen_US
dc.subjectPiece - wise - linear path - following algorithmsen_US
dc.subjectQuadratic penalty functionsen_US
dc.titlePiecewise-linear pathways to the optimal solution set in linear programmingen_US
dc.typeArticleen_US
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