M.Sc. Altangerel Lkhamsuren

A duality approach to gap functions for variational inequalities and equilibrium problems

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http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601214

Kurzfassung in Englisch

This work aims to investigate some applications of the
conjugate duality for scalar and vector optimization problems to
the construction of gap functions for variational inequalities and
equilibrium problems. The basic idea of the approach is to
reformulate variational inequalities and equilibrium problems into
optimization problems depending on a fixed variable, which allows
us to apply duality results from optimization problems.

Based on some perturbations, first we consider the conjugate
duality for scalar optimization. As applications, duality
investigations for the convex partially separable optimization
problem are discussed.

Afterwards, we concentrate our attention on some applications of
conjugate duality for convex optimization problems in finite and
infinite-dimensional spaces to the construction of a gap function
for variational inequalities and equilibrium problems. To verify
the properties in the definition of a gap function weak and strong
duality are used.

The remainder of this thesis deals with the extension of this
approach to vector variational inequalities and vector equilibrium
problems. By using the perturbation functions in analogy to the
scalar case, different dual problems for vector optimization and
duality assertions for these problems are derived. This study
allows us to propose some set-valued gap functions for the vector
variational inequality. Finally, by applying the Fenchel duality
on the basis of weak orderings, some variational principles for
vector equilibrium problems are investigated.

weitere Metadaten

Schlagwörter
Conjugate duality
Schlagwörter
Conjugate map
Schlagwörter
Duality for vector optimization
Schlagwörter
Equilibrium problems
Schlagwörter
Gap function
Schlagwörter
Variational inequalities
Schlagwörter
Variational principle
Schlagwörter
Vector equilibrium problems
Schlagwörter
Vector variational inequalities
SWD SchlagworteDualitätstheorie
SWD SchlagworteKonvexe Analysis
DDC Klassifikation510
Institution(en) 
HochschuleTU Chemnitz
FakultätFakultät für Mathematik
BetreuerProf. Dr. Gert Wanka
GutachterProf. Dr. Gert Wanka
Prof. Dr. Petra Weidner
Prof. Dr. Rentsen Enkhbat
DokumententypDissertation
SpracheEnglisch
Tag d. Einreichung (bei der Fakultät)12.04.2006
Tag d. Verteidigung / Kolloquiums / Prüfung25.07.2006
Veröffentlichungsdatum (online)03.08.2006
persistente URNurn:nbn:de:swb:ch1-200601214

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