An Augmented Lagrangian Method for Optimization Problems in Banach Spaces

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 allows the treatment of inequality constraints with infinite-dimensional image space. Mor...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Kanzow, Christian, Steck, Daniel, Wachsmuth, Daniel
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 12.07.2018
Subjects:
Algorithms
Banach spaces
Convexity
Lagrange multiplier
Nonlinear programming
Optimization
Viability
ISSN:2331-8422
Online Access:Get full text
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Summary: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 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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1807.04467