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Optimization Letters

, Volume 10, Issue 8, pp 1763–1779 | Cite as

Canonical duality for solving general nonconvex constrained problems

  • Vittorio Latorre
  • David Yang Gao
Original Paper

Abstract

This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems, a perfect dual problem (without duality gap) can be obtained in a unified form with global optimality conditions provided.While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints. Some fundamental concepts such as the objectivity and Lagrangian in nonlinear programming are addressed.

Keywords

Global optimization Nonlinear constrained programming  Augmented Lagrangian 

Notes

Acknowledgments

This research was supported by US Air Force Office of Scientific Research under the grant AFOSR FA9550-10-1-0487. Comments and suggestions from two anonymous referees are sincerely acknowledged.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Computer Control and Management EngineeringUniversity of Rome SapienzaRomeItaly
  2. 2.School of Science Information Technology and EngineeringFederation University AustraliaVictoriaAustralia

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