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Duality and Penalization in Optimization via an Augmented Lagrangian Function with Applications

  • Y. Y. Zhou
  • X. Q. Yang
Article

Abstract

This paper aims to establish duality and exact penalization results for the primal problem of minimizing an extended real-valued function in a reflexive Banach space in terms of a valley-at-0 augmented Lagrangian function. It is shown that every weak limit point of a sequence of optimal solutions generated by the valley-at-0 augmented Lagrangian problems is a solution of the original problem. A zero duality gap property and an exact penalization representation between the primal problem and the valley-at-0 augmented Lagrangian dual problem are obtained. These results are then applied to an inequality and equality constrained optimization problem in infinite-dimensional spaces and variational problems in Sobolev spaces, respectively.

Keywords

Valley-at-0 augmented Lagrangian function Zero duality gap Exact penalty function Reflexive Banach space 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsSoochow UniversitySoochowChina
  2. 2.Department of Applied MathematicsHong Kong Polytechnic UniversityKowloonChina

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