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We investigate the optimal configurations of n points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of theirapproximation ...
The minimum `1-norm solution to an underdetermined system of linear equations y = Ax, is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest i...
A number of problems in the analysis and design of control systems may be reformulated as the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices which depend affi...
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Zn. We present a semidefinite programming (SDP) method for obtaining a nontrivial lower bound on the ...
We present an ordinary differential equations approach to the analysis of algorithms for constructing l1 minimizing solutions to underdeter mined linear systems of full rank. It involves a relaxed min...
We consider sensor networks where energy is a limited resource so that energy consumption must be minimized while satisfying given throughput requirements. Moreover, energy consumption must take into ...
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
We consider the fundamental problem of estimating the mean of a vector y = Xβ + z, where X is an n× p design matrix in which one can have far more variables than observations and z is a stochastic err...
X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, and dual polarization interferometry, etc are indeed very powerful tools to determine the 3D structures of proteins (including the...
We consider a direct optimization approach for ensemble density functional theory electronic structure calculations. The update operator for the electronic orbitals takes the structure of the Stiefel ...
We consider a minimization scheme based on the Householder transport operator for the Grassman manifold, where a point on the manifold is represented by a m x n matrix with orthonormal columns. In par...
This article considers the problem of \min_{\xi}\vec{Pr}(\vert \xi^Tx\vert\leq \alpha)\quad s.t.\quad \Vert\xi\Vert_2=1. We first concentrate on the case that x_i,i=1,\cdots,n are binary random variab...
Abstract: In a distributed storage system, the storage costs of different storage nodes, in general, can be different. How to store a file in a given set of storage nodes so as to minimize the total s...
Abstract: The simplified Lennard-Jones (LJ) potential minimization problem is $f(x)=4\sum_{i=1}^N \sum_{j=1,j to} x\in \mathbb{R}^n,$ where...

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