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http://hdl.handle.net/10397/68643
Title: | Existence of augmented lagrange multipliers for semi-infinite programming problems | Authors: | Burachik, RS Yang, XQ Zhou, YY |
Issue Date: | May-2017 | Source: | Journal of optimization theory and applications, May 2017, v. 173, no. 2, p. 471-503 | Abstract: | Using an augmented Lagrangian approach, we study the existence of augmented Lagrange multipliers of a semi-infinite programming problem and discuss their characterizations in terms of saddle points. In the case of a sharp Lagrangian, we obtain a first-order necessary condition for the existence of an augmented Lagrange multiplier for the semi-infinite programming problem and some first-order sufficient conditions by assuming inf-compactness of the data functions and the extended Mangasarian-Fromovitz constraint qualification. Using a valley at 0 augmenting function and assuming suitable second-order sufficient conditions, we obtain the existence of an augmented Lagrange multiplier for the semi-infinite programming problem. | Keywords: | Semi-infinite programming Augmented Lagrange multiplier Optimality conditions Sharp Lagrangian A valley at 0 augmenting function |
Publisher: | Springer | Journal: | Journal of optimization theory and applications | ISSN: | 0022-3239 | EISSN: | 1573-2878 | DOI: | 10.1007/s10957-017-1091-6 | Rights: | © Springer Science+Business Media New York 2017 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10957-017-1091-6 |
Appears in Collections: | Journal/Magazine Article |
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Yang_Existence_Augmented_Lagrange.pdf | Pre-Published version | 888.41 kB | Adobe PDF | View/Open |
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