  


An Augmented Lagrangian Method for Conic Convex Programming
Necdet Serhat Aybat(nsa10psu.edu) Abstract: We propose a new firstorder augmented Lagrangian algorithm ALCC for solving convex conic programs of the form min{rho(x)+gamma(x): Axb in K, x in chi}, where rho and gamma are closed convex functions, and gamma has a Lipschitz continuous gradient, A is mxn real matrix, K is a closed convex cone, and chi is a "simple" convex compact set such that optimization problems of the form min{rho(x)+xx0_2^2: x in chi} can be efficiently solved for any given x0. We show that any limit point of the primal ALCC iterates is an optimal solution of the conic convex problem, and the dual ALCC iterates have a unique limit point that is a KarushKuhnTucker (KKT) point of the conic program. We also show that for any epsilon>0, the primal ALCC iterates are epsilon feasible and epsilonoptimal after O(log(1/epsilon)) iterations which require solving O(1/epsilon log(1/epsilon)) problems of the form min{rho(x)+xx0_2^2: x in chi}. Keywords: first order method, convex programming, conic constraints, augmented Lagrangian, convergence rate Category 1: Convex and Nonsmooth Optimization Category 2: Linear, Cone and Semidefinite Programming Citation: Download: [PDF] Entry Submitted: 02/26/2013 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  