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Duality

  • Mohammad Fathi
  • Hassan Bevrani
Chapter

Abstract

One common approach towards solving an optimization problem, in general, is to transfer it from the primal domain into a dual domain. This is sometimes of great advantage as the problem in the dual domain is simple enough to solve. In this chapter, this transformation is introduced and, based on the achievements from the dual domain, Karush–Kuhn–Tucker (KKT) conditions are derived to find optimal solutions in general optimization problems. Moreover, based on KKT conditions, Lagrangian algorithm is introduced to be implemented as an iterative search method to solve convex problems. Finally, some application examples in electrical engineering are given, accordingly.

Keywords

Duality Dual decomposition KKT conditions Lagrangian algorithm Sensitivity analysis 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mohammad Fathi
    • 1
  • Hassan Bevrani
    • 1
  1. 1.University of KurdistanKurdistanIran

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