In this paper several formulations and comparative test results are presented for problems involving the general paradigm of coupled sets of components. This paradigm is general enough to include systems of systems (SoS) ...

It is well-known by now that under suitable conditions L1 minimization can recover sparse solutions to under-determined linear systems of equations. More precisely, by solving the convex optimization problem min{||x||1 : ...

This thesis evaluates a method of computing highly accurate solutions for network simulations of integrate-and-fire (IAF) neurons. Simulations are typically evolved using time-stepping, but since the IAF model is composed ...

This thesis presents spectral zero selection criteria for a rigorous theory on passivity preserving model reduction via interpolation of spectral zeros. For linear time invariant systems in circuit simulation, passivity ...

This paper describes a Parallel Space Decomposition (PSD) technique for the Mesh Adaptive Direct Search (MADS) algorithm. MADS extends Generalized Pattern Search for constrained nonsmooth optimization problems. The objective ...

We propose a new algorithm for general constrained derivative-free optimization. As in most methods, constraint violations are aggregated into a single constraint violation function. As in filter methods, a threshold, or ...

The symmetry preserving singular value decomposition (SPSVD) produces the best symmetric (low rank) approximation to a set of data. These symmetric approximations are characterized via an invariance under the action of a ...

The goal of this paper is to combine balanced truncation model reduction and domain decomposition to derive reduced order models with guaranteed error bounds for systems of discretized partial differential equations (PDEs) ...

This thesis concentrates on the development, analysis, implementation, and application of a symmetry preserving singular value decomposition (SPSVD). This new factorization enhances the singular value decomposition (SVD)---a ...

We consider solving minimization problems with L_1-regularization: min ||x||_1 + mu f(x) particularly for f(x) = (1/2)||Ax-b||M2, where A is m by n and m < n. Our goal is to construct efficient and robust algorithms for ...