joint work with Ning Zhang, Defeng Sun, Kim-Chuan Toh
This paper focuses on the fused multiple graphical Lasso model. For solving the model, we develop an efficient regularized proximal point algorithm, where the subproblem in each iteration of the algorithm is solved by a superlinearly convergent semismooth Newton method. To implement the method, we derive an explicit expression for the generalized Jacobian of the proximal mapping of the fused multiple graphical Lasso regularizer. Our approach has exploited the underlying second order information. The efficiency and robustness of our proposed algorithm are shown by numerical experiments.
joint work with Defeng Sun, Kim-Chuan Toh
We propose a semi-proximal augmented Lagrangian based decomposition method for convex composite quadratic conic programming problems with primal block angular structures. Using our algorithmic framework, we are able to naturally derive several well-known augmented Lagrangian based decomposition methods for stochastic programming such as the diagonal quadratic approximation method of Mulvey and Ruszczynski. We also propose a semi-proximal symmetric Gauss-Seidel based alternating direction method of multipliers for solving the corresponding dual problem.
joint work with Jia Li, Defeng Sun, Kim-Chuan Toh
In this talk, we consider the problem of computing a Wasserstein barycenter for a set of discrete distributions with finite supports. When the supports in the barycenter are prespecified, this problem is essentially a large-scale linear programming (LP). To handle this LP, we derive its dual problem and adapt a symmetric Gauss-Seidel based ADMM. The global linear convergence rate is also given without any condition. All subproblems involved can be solved exactly and efficiently. Numerical experiments show that our method is more efficient than two existing representative methods and Gurobi.