New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization

C. Gutiérrez (), B. Jiménez () and V. Novo ()
Additional contact information
C. Gutiérrez: Universidad de Valladolid
B. Jiménez: Universidad Nacional de Educación a Distancia
V. Novo: Universidad Nacional de Educación a Distancia

Journal of Optimization Theory and Applications, 2009, vol. 142, issue 1, No 5, 85-106

Abstract: Abstract We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied.

Keywords: Second order directional derivative; Optimality conditions; Vector optimization; Scalarization; Second order tangent set (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-009-9525-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:142:y:2009:i:1:d:10.1007_s10957-009-9525-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-009-9525-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().