Existence of augmented Lagrange multipliers for cone constrained optimization problems

In this paper, by using an augmented Lagrangian approach, we obtain several sufficient conditions for the existence of augmented Lagrange multipliers of a cone constrained optimization problem in Banach spaces, where the corresponding augmenting function is assumed to have a valley at zero. Furtherm...

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Bibliographic Details
Published in:Journal of global optimization 2014-02, Vol.58 (2), p.243-260
Main Authors: Zhou, Yu Ying, Zhou, Jin Chuan, Yang, Xiao Qi
Format: Article
Language:English
Subjects:
Applied mathematics
Banach space
Banach spaces
Computer Science
Constraints
Lagrange multiplier
Lagrange multipliers
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Optimization algorithms
Quadratic programming
Real Functions
Saddle points
Science
Studies
Valleys
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Summary:In this paper, by using an augmented Lagrangian approach, we obtain several sufficient conditions for the existence of augmented Lagrange multipliers of a cone constrained optimization problem in Banach spaces, where the corresponding augmenting function is assumed to have a valley at zero. Furthermore, we deal with the relationship of saddle points, augmented Lagrange multipliers, and zero duality gap property between the cone constrained optimization problem and its augmented Lagrangian dual problem.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-013-0046-1