Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24298
Title: Duality and penalization in optimization via an augmented Lagrangian function with applications
Authors: Zhou, YY
Yang, XQ 
Keywords: Exact penalty function
Reflexive Banach space
Valley-at-0 augmented Lagrangian function
Zero duality gap
Issue Date: 2009
Publisher: Springer
Source: Journal of optimization theory and applications, 2009, v. 140, no. 1, p. 171-188 How to cite?
Journal: Journal of optimization theory and applications 
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.
URI: http://hdl.handle.net/10397/24298
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-008-9455-6
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