Some Properties of the Augmented Lagrangian in Cone Constrained Optimization

Authors:
Alexander Shapiro;Jie Sun
Affiliations:
-;-
Venue:
Mathematics of Operations Research
Year:
2004

Citing 0
Cited 5

Alternating direction method for bi-quadratic programming

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Weak stability and strong duality of a class of nonconvex infinite programs via augmented Lagrangian

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On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming

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Generalized weak sharp minima in cone-constrained convex optimization with applications

Computational Optimization and Applications
Existence of augmented Lagrange multipliers for cone constrained optimization problems

Journal of Global Optimization

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Abstract

A large class of optimization problems can be modeled as minimization of an objective function subject to constraints given in a form of set inclusions. In this paper, we discuss augmented Lagrangian duality for such optimization problems. We formulate the augmented Lagrangian dual problems and study conditions ensuring existence of the corresponding augmented Lagrange multipliers. We also discuss sensitivity of optimal solutions to small perturbations of augmented Lagrange multipliers.