On the rate analysis of inexact augmented Lagrangian schemes for convex optimization problems with misspecified constraints

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Abstract

We consider a misspecified optimization problem that requires minimizing of a convex function f (x;θ∗) in x over a constraint set represented by h(x;θ) ≤ 0 where θ∗ is an unknown (or misspecified) vector of parameters. Suppose θ∗ is learnt by a distinct process that generates a sequence of estimators θk, each of which is an increasingly accurate approximation of θ∗. We develop a first-order augmented Lagrangian scheme for computing an optimal solution x∗ while simultaneously learning θ∗.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4841-4846
Number of pages6
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Publication series

NameProceedings of the American Control Conference
Volume2016-July
ISSN (Print)0743-1619

Other

Other2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period7/6/167/8/16

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All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Ahmadi, H., Aybat, N. S., & Shanbhag, U. V. (2016). On the rate analysis of inexact augmented Lagrangian schemes for convex optimization problems with misspecified constraints. In 2016 American Control Conference, ACC 2016 (pp. 4841-4846). [7526119] (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7526119