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The Fundamental Relations between Geometric Programming Duality, Parametric Programming Duality, and Ordinary Lagrangian Duality

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Abstract

Every formulation of mathematical programming duality (known to the author) for continuous finite-dimensional optimization can easily be viewed as a special case of at least one of the following three formulations: the geometric programming formulation (of the generalized geometric programming type), the parametric programming formulation (of the generalized Rockafellar-perturbation type), and the ordinary Lagrangian formulation (of the generalized Falk type). The relative strengths and weaknesses of these three duality formulations are described herein, as are the fundamental relations between them. As a theoretical application, the basic duality between Fenchel's hypothesis and the existence of recession directions in convex programming is established and then expressed within each of these three duality formulations

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  1. Department of Mathematics, and Graduate Program in Operations Research, North Carolina State University, Raleigh, NC, 27695, USA

    Elmor L. Peterson

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Peterson, E.L. The Fundamental Relations between Geometric Programming Duality, Parametric Programming Duality, and Ordinary Lagrangian Duality. Annals of Operations Research 105, 109–153 (2001). https://doi.org/10.1023/A:1013353515966

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