We shall describe many other valu- able applications of duality theory in this chapter as well.One of the key uses of duality theory lies in the interpretation and implementation of sensitivity analysis. As we
"Using Duality Theory for Identification of Primal Efficient Points and for Sensitivity Analysis in Multiple Objective Linear Programming," J. of the Operational Research Society, 29(7), 1978, 643-649.Hannan, E.L., 1978. Using duality theory for identification of primal efficient points and for...
Georgia Institute of Technology, School of Industrial and Systems Engineering, Atlanta, GeorgiaHanif D. SheraliVirginia Polytechnic Institute and State University, Grado Department of Industrial and Systems Engineering, Blacksburg, VirginiaWageningen Academic PublishersDecision Sciences Theory & Applications...
Duality theory is a rich and powerful area of convex optimization, and central to understanding sensitivity analysis and infeasibility issues. Furthermore, it provides a simple and systematic way of obtaining non-trivial lower bounds on the optimal value for many difficult non-convex problems....
Chapter3Dualitytheory AnimportantdiscoveryintheearlydevelopmentofLP isDualityTheory. EachLPproblem,referredtoas“aprimalproblem”is associatedwithanotherLPproblemcalled“adual problem”. Oneofthekeyusesofdualitytheoryliesinthe interpretationandimplementationofsensitivityanalysis. TheessenceofDualityTheoryTheessenceof...
Proof. This can be shown in each case by the stand- ard operations of duality theory and the full proof is hence omitted. Remark 4. The ENGP variant, Equations (46)–(52), reduces to the WGP model when L ¼ 1 and a ¼ 0. Proof. Let L ¼ 1 and a ¼ 0. Then: ...
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and ...
Here its solutions are characterized using Banach space duality theory, and shown to be allpass. The results are applied to the optimization of weighted sensitivity to disturbances, in feedback systems subject to large plant-uncertainty.Access through your organization Check access to the full text ...
(2022) developed a robust fractional DEA model and showed, using duality theory, that the primal worst-case possible data in the multiplier model is equivalent to the dual best-case possible data in the envelopment model. By employing robust DEA, Hatami-Marbini et al. (2022a) presented a ...
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and ...