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This book investigates several duality approaches for vector
optimization problems, while also comparing them. Special attention
is paid to duality for linear vector optimization problems, for
which a vector dual that avoids the shortcomings of the classical
ones is proposed. Moreover, the book addresses different efficiency
concepts for vector optimization problems. Among the problems that
appear when the framework is generalized by considering set-valued
functions, an increasing interest is generated by those involving
monotone operators, especially now that new methods for approaching
them by means of convex analysis have been developed. Following
this path, the book provides several results on different
properties of sums of monotone operators.
This book investigates several duality approaches for vector
optimization problems, while also comparing them. Special attention
is paid to duality for linear vector optimization problems, for
which a vector dual that avoids the shortcomings of the classical
ones is proposed. Moreover, the book addresses different efficiency
concepts for vector optimization problems. Among the problems that
appear when the framework is generalized by considering set-valued
functions, an increasing interest is generated by those involving
monotone operators, especially now that new methods for approaching
them by means of convex analysis have been developed. Following
this path, the book provides several results on different
properties of sums of monotone operators.
Thecontinuousandincreasinginterestconcerningvectoroptimizationperc-
tible in the research community, where contributions dealing with
the theory of duality abound lately, constitutes the main
motivation that led to writing this book. Decisive was also the
research experience of the authors in this ?eld, materialized in a
number of works published within the last decade. The need for a
book on duality in vector optimization comes from the fact that
despite the large amount of papers in journals and proceedings
volumes, no book mainly concentrated on this topic was available so
far in the scienti?c landscape. There is a considerable presence of
books, not all recent releases, on vector optimization in the
literature. We mention here the ones due to Chen,HuangandYang(cf.
[49]),EhrgottandGandibleux(cf. [65]),Eichfelder (cf. [66]), Goh and
Yang (cf. [77]), G.. opfert and Nehse (cf. [80]), G.. opfert, -
ahi, Tammer and Z? alinescu (cf. [81]), Jahn (cf. [104]),
Kaliszewski (cf. [108]), Luc (cf. [125]), Miettinen (cf. [130]),
Mishra, Wang and Lai (cf. [131,132]) and Sawaragi, Nakayama and
Tanino (cf. [163]), where vector duality is at most tangentially
treated. We hope that from our e?orts will bene? t not only
researchers interested in vector optimization, but also graduate
and und- graduate students. The framework we consider is taken as
general as possible, namely we work in (locally convex) topological
vector spaces, going to the usual ?nite - mensional setting when
this brings additional insights or relevant connections to the
existing literature.
Thecontinuousandincreasinginterestconcerningvectoroptimizationperc-
tible in the research community, where contributions dealing with
the theory of duality abound lately, constitutes the main
motivation that led to writing this book. Decisive was also the
research experience of the authors in this ?eld, materialized in a
number of works published within the last decade. The need for a
book on duality in vector optimization comes from the fact that
despite the large amount of papers in journals and proceedings
volumes, no book mainly concentrated on this topic was available so
far in the scienti?c landscape. There is a considerable presence of
books, not all recent releases, on vector optimization in the
literature. We mention here the ones due to Chen,HuangandYang(cf.
[49]),EhrgottandGandibleux(cf. [65]),Eichfelder (cf. [66]), Goh and
Yang (cf. [77]), G.. opfert and Nehse (cf. [80]), G.. opfert, -
ahi, Tammer and Z? alinescu (cf. [81]), Jahn (cf. [104]),
Kaliszewski (cf. [108]), Luc (cf. [125]), Miettinen (cf. [130]),
Mishra, Wang and Lai (cf. [131,132]) and Sawaragi, Nakayama and
Tanino (cf. [163]), where vector duality is at most tangentially
treated. We hope that from our e?orts will bene? t not only
researchers interested in vector optimization, but also graduate
and und- graduate students. The framework we consider is taken as
general as possible, namely we work in (locally convex) topological
vector spaces, going to the usual ?nite - mensional setting when
this brings additional insights or relevant connections to the
existing literature.
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