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FenchelLagrange versus Geometric Duality in Convex Optimization
"... We present a new duality theory in order to treat convex optimization problems and we prove that the geometric duality used by C.H. Scott and T.R. Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions in order to achieve st ..."
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Cited by 5 (4 self)
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We present a new duality theory in order to treat convex optimization problems and we prove that the geometric duality used by C.H. Scott and T.R. Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions in order to achieve strong duality are considered and optimality conditions are derived. Next we apply our approach to some problems considered by Scott and Jefferson, determining their duals. We give weaker sufficient conditions in order to achieve strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a particular case of the duality approach we present.
Duality for composed convex functions with applications in location theory
 MultiCriteria und FuzzySysteme in Theorie und Praxis”, Deutscher UniversitätsVerlag
, 2003
"... location theory ..."
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Bibliographical description
"... Farkas type results for convex and non convex inequality systems Von der Fakultät für Mathematik der Technischen Universität Chemnitz genehmigte D i s s e r t a t i o n zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.) vorgelegt von Dipl. Math. Ioan Bogdan Hodrea ge ..."
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Farkas type results for convex and non convex inequality systems Von der Fakultät für Mathematik der Technischen Universität Chemnitz genehmigte D i s s e r t a t i o n zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.) vorgelegt von Dipl. Math. Ioan Bogdan Hodrea geboren am 11.03.1979 in Baia Mare (Rumänien) eingereicht am 01.10.07
To my parents Bibliographical description
, 2003
"... multiobjective optimization ..."
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Multiobjective
"... duality for convex semidefinite programming problems G. Wanka, R.I. Bot ¸ and S.M. Grad Abstract. We treat some duality assertions regarding multiobjective convex semidefinite programming problems. Having a vector minimization problem with convex entries in the objective vector function, we establis ..."
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duality for convex semidefinite programming problems G. Wanka, R.I. Bot ¸ and S.M. Grad Abstract. We treat some duality assertions regarding multiobjective convex semidefinite programming problems. Having a vector minimization problem with convex entries in the objective vector function, we establish a dual for it using the socalled conjugacy approach. In order to deal with the duality assertions between these problems we need to study the duality properties and the optimality conditions of the scalarized problem associated to the initial one. Using these results we present the weak, strong and converse duality assertions regarding the primal problem and the dual we obtained for it. Keywords: multiobjective duality, semidefinite programming, Paretoefficiency, convex optimization AMS subject classification: Primary 49N15, secondary 90C22, 90C25, 90C29 1.
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"... Duality for multiobjective optimization problems with convex objective functions and D.C. constraints ..."
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Duality for multiobjective optimization problems with convex objective functions and D.C. constraints