On quadratic scalarization of vector optimization problems in Banach spaces

We study vector optimization problems in partially ordered Banach spaces and suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the so-called adaptive scalarization of such problems and sho...

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Bibliographic Details
Published in:Applicable analysis Vol. 93; no. 5; pp. 994 - 1009
Main Authors: Kogut, Peter I., Manzo, Rosanna
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.05.2014
Taylor & Francis Ltd
Subjects:
Approximation
Banach space
Banach spaces
efficient solutions
lower semicontinuity
Mapping
Mathematical analysis
Mathematical problems
Nonlinearity
Optimization
Optimization techniques
partial-ordered spaces
Quadratic programming
scalarization approach
Scalars
Vector space
vector-valued optimization
Vectors (mathematics)
ISSN:0003-6811, 1563-504X
Online Access:Get full text
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Summary:We study vector optimization problems in partially ordered Banach spaces and suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the so-called adaptive scalarization of such problems and show that the corresponding scalar non-linear optimization problems can be by-turn approximated by quadratic minimization problems.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2013.809068