Aufgrund von Vorbereitungen auf eine neue Version von KOPS, können kommenden Montag und Dienstag keine Publikationen eingereicht werden. (Due to preparations for a new version of KOPS, no publications can be submitted next Monday and Tuesday.)
Type of Publication: | Journal article |
Author: | Schweighofer, Markus; Klep, Igor |
Year of publication: | 2013 |
Published in: | Mathematics of Operations Research ; 38 (2013), 3. - pp. 569-590. - ISSN 0364-765X. - eISSN 1526-5471 |
DOI (citable link): | https://dx.doi.org/10.1287/moor.1120.0584 |
Summary: |
Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebraic certificates for all infeasible linear matrix inequalities in the spirit of real algebraic geometry: A linear matrix inequality A(x) >_ 0 is infeasible if and only if −1 lies in the quadratic module associated to A. We also present a new exact duality theory for semidefinite programming, motivated by the real radical and sums of squares certificates from real algebraic geometry.
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Subject (DDC): | 510 Mathematics |
Keywords: | linear matrix inequality, LMI, spectrahedron, semidefinite programming, SDP, quadratic module, infeasibility, duality theory, real radical, Farkas' lemma |
Bibliography of Konstanz: | Yes |
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SCHWEIGHOFER, Markus, Igor KLEP, 2013. An exact duality theory for semidefinite programming based on sums of squares. In: Mathematics of Operations Research. 38(3), pp. 569-590. ISSN 0364-765X. eISSN 1526-5471. Available under: doi: 10.1287/moor.1120.0584
@article{Schweighofer2013exact-24805, title={An exact duality theory for semidefinite programming based on sums of squares}, year={2013}, doi={10.1287/moor.1120.0584}, number={3}, volume={38}, issn={0364-765X}, journal={Mathematics of Operations Research}, pages={569--590}, author={Schweighofer, Markus and Klep, Igor} }