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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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 156; no. 3; pp. 683 - 700
Main Authors: Rodríguez-Marín, Luis, Sama, Miguel
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2013
Springer Nature B.V
Subjects:
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
Lagrange multiplier rules
Set-valued optimization
Vector optimization
Contingent (epi)derivatives
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0154-y