Duality for semi-definite and semi-infinite programming

In this article, we study semi-definite and semi-infinite programming problems (SDSIP), which includes semi-infinite linear programs and semi-definite programs as special cases. We establish that a uniform duality between the homogeneous (SDSIP) and its Lagrangian-type dual problem is equivalent to...

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Bibliographic Details
Published inOptimization Vol. 52; no. 4-5; pp. 507 - 528
Main Authors Li, S.J., Yang, X.Q., Teo, K.L.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.08.2003
Subjects
Duality
Mathematics Subject Classifications 2000: 49N15
Semi-definite program
Semi-infinite program
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ISSN0233-1934
1029-4945
DOI10.1080/02331930310001611484

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Summary:In this article, we study semi-definite and semi-infinite programming problems (SDSIP), which includes semi-infinite linear programs and semi-definite programs as special cases. We establish that a uniform duality between the homogeneous (SDSIP) and its Lagrangian-type dual problem is equivalent to the closedness condition of certain cone. Moreover, this closedness condition was assured by a generalized canonically closedness condition and a Slater condition. Corresponding results for the nonhomogeneous (SDSIP) problem were obtained by transforming it into an equivalent homogeneous (SDSIP) problem.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331930310001611484