991 research outputs found
A Scalable and Extensible Framework for Superposition-Structured Models
In many learning tasks, structural models usually lead to better
interpretability and higher generalization performance. In recent years,
however, the simple structural models such as lasso are frequently proved to be
insufficient. Accordingly, there has been a lot of work on
"superposition-structured" models where multiple structural constraints are
imposed. To efficiently solve these "superposition-structured" statistical
models, we develop a framework based on a proximal Newton-type method.
Employing the smoothed conic dual approach with the LBFGS updating formula, we
propose a scalable and extensible proximal quasi-Newton (SEP-QN) framework.
Empirical analysis on various datasets shows that our framework is potentially
powerful, and achieves super-linear convergence rate for optimizing some
popular "superposition-structured" statistical models such as the fused sparse
group lasso
Integrated risk/cost planning models for the US Air Traffic system
A prototype network planning model for the U.S. Air Traffic control system is described. The model encompasses the dual objectives of managing collision risks and transportation costs where traffic flows can be related to these objectives. The underlying structure is a network graph with nonseparable convex costs; the model is solved efficiently by capitalizing on its intrinsic characteristics. Two specialized algorithms for solving the resulting problems are described: (1) truncated Newton, and (2) simplicial decomposition. The feasibility of the approach is demonstrated using data collected from a control center in the Midwest. Computational results with different computer systems are presented, including a vector supercomputer (CRAY-XMP). The risk/cost model has two primary uses: (1) as a strategic planning tool using aggregate flight information, and (2) as an integrated operational system for forecasting congestion and monitoring (controlling) flow throughout the U.S. In the latter case, access to a supercomputer is required due to the model's enormous size
A distributed primal-dual interior-point method for loosely coupled problems using ADMM
In this paper we propose an efficient distributed algorithm for solving
loosely coupled convex optimization problems. The algorithm is based on a
primal-dual interior-point method in which we use the alternating direction
method of multipliers (ADMM) to compute the primal-dual directions at each
iteration of the method. This enables us to join the exceptional convergence
properties of primal-dual interior-point methods with the remarkable
parallelizability of ADMM. The resulting algorithm has superior computational
properties with respect to ADMM directly applied to our problem. The amount of
computations that needs to be conducted by each computing agent is far less. In
particular, the updates for all variables can be expressed in closed form,
irrespective of the type of optimization problem. The most expensive
computational burden of the algorithm occur in the updates of the primal
variables and can be precomputed in each iteration of the interior-point
method. We verify and compare our method to ADMM in numerical experiments.Comment: extended version, 50 pages, 9 figure
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