  


How the augmented Lagrangian algorithm can deal with an infeasible convex quadratic optimization problem
Alice Chiche(Alice.Chicheartelys.com) Abstract: This paper analyses the behavior of the augmented Lagrangian algorithm when it deals with an infeasible convex quadratic optimization problem. It is shown that the algorithm finds a point that, on the one hand, satisfies the constraints shifted by the smallest possible shift that makes them feasible and, on the other hand, minimizes the objective on the corresponding shifted constrained set. The speed of convergence to such a point is globally linear, with a rate that is inversely proportional to the augmentation parameter. This suggests us a rule for determining the augmentation parameter that aims at controlling the speed of convergence of the shifted constraint norm to zero; this rule has the advantage of generating bounded augmentation parameters even when the problem is infeasible. Keywords: augmented Lagrangian algorithm, augmentation parameter update, closest feasible problem, convex quadratic optimization, feasible shift, global linear convergence, infeasible problem, proximal point algorithm, quasiglobal error bound, shifted constraint Category 1: Nonlinear Optimization (Quadratic Programming ) Category 2: Convex and Nonsmooth Optimization Citation: INRIA Research Report RR8583 (August 23, 2014). INRIA ParisRocquencourt, Pomdapi team  BP 105, F78153 Le Chesnay Cedex (France). Download: [PDF] Entry Submitted: 08/25/2014 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  