Duality and penalization in optimization via an augmented Lagrangian function with applications

Y. Y. Zhou, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)171-188
Number of pages18
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - 1 Jan 2009


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

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research


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