Abstract

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions, and it allows the treatment of inequality constraints with infinite-dimensional image space. Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global optimality, and KKT conditions. Some numerical results are given to illustrate the practical viability of the method.

Keywords

  1. constrained optimization
  2. augmented Lagrangian method
  3. Banach space
  4. inequality constraints
  5. global convergence

MSC codes

  1. 49M20
  2. 65K10
  3. 90C48

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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 272 - 291
ISSN (online): 1095-7138

History

Submitted: 7 December 2016
Accepted: 5 December 2017
Published online: 1 February 2018

Keywords

  1. constrained optimization
  2. augmented Lagrangian method
  3. Banach space
  4. inequality constraints
  5. global convergence

MSC codes

  1. 49M20
  2. 65K10
  3. 90C48

Authors

Affiliations

Funding Information

Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : KA 1296/24-1, Wa 3626/3-1

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