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

Y. Y. Zhou () and X. Q. Yang
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Y. Y. Zhou: Soochow University
X. Q. Yang: Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2009, vol. 140, issue 1, No 11, 188 pages

Abstract: 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 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-008-9455-6

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