On asymptotic Lagrangian duality for nonsmooth optimization

Regina S Burachik


Zero duality gap for nonconvex optimization problems requires the use of a generalized Lagrangian function in the definition of the dual problem. We analyze the situation in which the original problem is associated with a sequence of Lagrangian functions, which in turn defines a sequence of dual problems. Under a set of basic assumptions, we prove that the generated sequence of optimal dual values converges to the optimal primal value, and call the latter situation strong duality for the sequence of Lagrangian functions. As an application of our theory, we construct two sequences of augmented Lagrangians for general equality constrained optimization problems in finite dimensions which exhibit strong duality in this new sense.

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Nonconvex Duality, Lagrangian function, augmented Lagrangian, valley at zero, asymptotic duality

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DOI: http://dx.doi.org/10.21914/anziamj.v58i0.11874

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