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SIAMJO
2011
13 years 4 months ago
Minimizing the Condition Number of a Gram Matrix
Abstract. The condition number of a Gram matrix defined by a polynomial basis and a set of points is often used to measure the sensitivity of the least squares polynomial approxim...
Xiaojun Chen, Robert S. Womersley, Jane J. Ye
SIAMJO
2011
13 years 4 months ago
A Unifying Polyhedral Approximation Framework for Convex Optimization
Abstract. We propose a unifying framework for polyhedral approximation in convex optimization. It subsumes classical methods, such as cutting plane and simplicial decomposition, bu...
Dimitri P. Bertsekas, Huizhen Yu
SIAMJO
2011
13 years 4 months ago
Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization
We present a class of inexact adaptive multilevel trust-region SQP-methods for the efficient solution of optimization problems governed by nonlinear partial differential equations...
J. Carsten Ziems, Stefan Ulbrich
SIAMJO
2011
13 years 4 months ago
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
Many applications arising in a variety of fields can be well illustrated by the task of recovering the low-rank and sparse components of a given matrix. Recently, it is discovered...
Min Tao, Xiaoming Yuan
SIAMJO
2011
13 years 18 days ago
Rank-Sparsity Incoherence for Matrix Decomposition
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-ran...
Venkat Chandrasekaran, Sujay Sanghavi, Pablo A. Pa...