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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Vydáno v:Journal of optimization theory and applications Ročník 156; číslo 3; s. 683 - 700
Hlavní autoři: Rodríguez-Marín, Luis, Sama, Miguel
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.03.2013
Springer Nature B.V
Témata:
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
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Shrnutí: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