Fenchel-Lagrange Duality Versus Geometric Duality in Convex Optimization

R. I. Boţ, S. M. Grad and G. Wanka
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R. I. Boţ: Chemnitz University of Technology
S. M. Grad: Chemnitz University of Technology
G. Wanka: Chemnitz University of Technology

Journal of Optimization Theory and Applications, 2006, vol. 129, issue 1, No 3, 33-54

Abstract: Abstract We present a new duality theory to treat convex optimization problems and we prove that the geometric duality used by Scott and Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions 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 to achieve strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a particular case of the duality approach that we present.

Keywords: Geometric programming; convex optimization; perturbation theory; Lagrange and Fenchel duality; conjugate functions (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-006-9047-2

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