Some Properties of the Augmented Lagrangian in Cone Constrained Optimization

Alexander Shapiro, Jie Sun
2004 Mathematics of Operations Research  
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.
doi:10.1287/moor.1040.0103 fatcat:n4o5nm3a3vhzraeni7god4gwze