Practical augmented Lagrangian methods for constrained optimization

By Ernesto G. Birgin, Jose Mario Martínez. Fundamentals of algorithms, 2014

515 citations recorded by the source corpus.

Subfields: Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/aca30e5c9ecdac0254584616d061cf02ae99305c

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In Numerical Analysis

1. Jinshan Zeng
2. Yu Wang
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4. Ming Yan
5. Yangyang Xu
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8. Antonin Chambolle

Citations in the corpus

• Challenges and opportunities in quantum optimization (2023, unknown): “Such Lagrangian methods are well understood 130,131 , but global-convergence results are limited by very restrictive conditions, in general, or require some form of backtracking 132 .”
• Global Convergence of ADMM in Nonconvex Nonsmooth Optimization (2015, methodology): “ i=1 r(x) + Xp i=1 li(Aizi −bi), (43a) subject to Ex+ Inpz= 0. (43b) where E = −[In;...;In] ∈ Rnp×n, Inp ∈ Rnp×np is the identity matrix, and z = [z 1;...;zp] ∈ Rnp. Fitting (43) to the standard form (5), there are two blocks (Px,z) and B= Inp. f(x) = r(x) and h(z) = p i=1li(Aizi −bi). Now let us ch”