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A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions II: Extended Exactness. (arXiv:1710.01961v1 [math.OC])
来源于:arXiv
In the second paper of the series we introduce the concept of the global
extended exactness of penalty and augmented Lagrangian functions, and derive
the localization principle in the extended form. The main idea behind the
extended exactness consists in the extension of the original constrained
optimization problem by adding some extra variables, and then the construction
of a penalty/augmented Lagrangian function for the extended problem. This
approach allows one to design extended penalty/augmented Lagrangian functions
having some useful properties (such as smoothness), which their counterparts
for the original problem might not possess. In turn, the global exactness of
such extended functions can be easily proved with the use of the localization
principle presented in this paper, which reduces the study of global exactness
to a local analysis of sufficient optimality conditions and constraint
qualifications. We utilize the localization principle in order to obtain simple
necessary 查看全文>>