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Boţ, Radu Ioan; Grad, Sorin Mihai; Wanka, Gert : Fenchel-Lagrange versus Geometric Duality in Convex Optimization

Boţ, Radu Ioan ; Grad, Sorin Mihai ; Wanka, Gert : Fenchel-Lagrange versus Geometric Duality in Convex Optimization

Author(s):
Boţ, Radu Ioan
Grad, Sorin Mihai
Wanka, Gert
Title:
Fenchel-Lagrange versus Geometric Duality in Convex Optimization
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 2, 2005
Mathematics Subject Classification:
49N15 [ Duality theory ]
90C25 [ Convex programming ]
90C46 [ Optimality conditions, duality ]
Abstract:
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 in each case. Next we apply our approach to some problems considered by Scott and Jefferson determining their duals. We give some 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.
Keywords:
geometric programming, convex optimization, Lagrange and Fenchel duality, conjugate functions
Language:
English
Publication time:
1 / 2005