Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces
This paper deals with Lagrange multiplier rules for constrained set-valued optimization problems in infinite-dimensional spaces, where the multipliers appear as scalarization functions of the maps instead of the derivatives. These rules provide necessary conditions for weak minimizers under hypothes...
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| Veröffentlicht in: | Journal of optimization theory and applications Jg. 156; H. 3; S. 683 - 700 |
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01.03.2013
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| Abstract | This paper deals with Lagrange multiplier rules for constrained set-valued optimization problems in infinite-dimensional spaces, where the multipliers appear as scalarization functions of the maps instead of the derivatives. These rules provide necessary conditions for weak minimizers under hypotheses of stability, convexity, and directional compactness. Counterexamples show that the hypotheses are minimal. |
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| AbstractList | This paper deals with Lagrange multiplier rules for constrained set-valued optimization problems in infinite-dimensional spaces, where the multipliers appear as scalarization functions of the maps instead of the derivatives. These rules provide necessary conditions for weak minimizers under hypotheses of stability, convexity, and directional compactness. Counterexamples show that the hypotheses are minimal. This paper deals with Lagrange multiplier rules for constrained set-valued optimization problems in infinite-dimensional spaces, where the multipliers appear as scalarization functions of the maps instead of the derivatives. These rules provide necessary conditions for weak minimizers under hypotheses of stability, convexity, and directional compactness. Counterexamples show that the hypotheses are minimal.[PUBLICATION ABSTRACT] |
| Author | Rodríguez-Marín, Luis Sama, Miguel |
| Author_xml | – sequence: 1 givenname: Luis surname: Rodríguez-Marín fullname: Rodríguez-Marín, Luis organization: Departamento de Matemática Aplicada, E.T.S.I.I. Universidad Nacional de Educación a Distancia – sequence: 2 givenname: Miguel surname: Sama fullname: Sama, Miguel email: msama@ind.uned.es organization: Departamento de Matemática Aplicada, E.T.S.I.I. Universidad Nacional de Educación a Distancia |
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| CitedBy_id | crossref_primary_10_1007_s11117_021_00842_5 crossref_primary_10_1007_s11590_013_0690_x crossref_primary_10_1007_s11590_021_01722_3 crossref_primary_10_1016_j_na_2014_04_022 crossref_primary_10_1007_s00025_024_02182_8 |
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| Keywords | Lagrange multiplier rules Set-valued optimization Vector optimization Contingent (epi)derivatives |
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| SubjectTerms | Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Constraints Control theory Derivatives Engineering Hypotheses Lagrange multiplier Lagrange multipliers Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Partial differential equations Scalars Stability Theory of Computation |
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| Title | Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces |
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