A unified nonlinear augmented Lagrangianapproach for nonconvex vector optimization

Chunrong Chen

doi:10.3934/naco.2011.1.495

Article Contents

2011, Volume 1, Issue 3: 495-508. Doi: 10.3934/naco.2011.1.495

This issue Previous Article A note on monotone approximations of minimum and maximum functions and multi-objective problems Next Article A primal-dual algorithm for nonlinear programming exploiting negative curvature directions

A unified nonlinear augmented Lagrangian approach for nonconvex vector optimization

Chunrong Chen^1,

1.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331

Received: March 31, 2011

Revised: June 30, 2011

Published: August 2011

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Abstract

In this paper, we propose a unified nonlinear augmented Lagrangian dual approach for a nonconvex vector optimization problem by applying a class of vector-valued nonlinear augmented Lagrangian penalty functions. We establish weak and strong duality results, necessary and sufficient conditions for uniformly exact penalization and exact penalization in the framework of nonlinear augmented Lagrangian.

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Mathematics Subject Classification: Primary: 90C29; Secondary: 90C46.

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References

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