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24 June 2024
 
  » arxiv » 2302.00363

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Implicit augmented Lagrangian and generalized optimization
Alberto De Marchi ;
Date 1 Feb 2023
AbstractGeneralized nonlinear programming is considered in the fully nonconvex setting, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and nonlinear, set-membership constraints. The augmented Lagrangian framework is extended to this broad problem class, preserving an implicit formulation and treating slack variables merely as a formal device. Based on parametric optimization and variational analysis notions, a tailored stationarity concept is devised to better qualify the iterates, generated as approximate solutions to a sequence of subproblems. Using this sharp characterization and a lifted reformulation, a suitable multiplier update rule is derived, while asymptotic properties and convergence guarantees are established for a safeguarded augmented Lagrangian scheme. A numerical example indicates the benefits of the advocated implicit approach.
Source arXiv, 2302.00363
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