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A primal-dual potential reduction method for problems involving matrix inequalities
Interior point algorithms Linear matrix inequaliües Semidefinite programming
2015/8/11
We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga ...
A new graph parameter related to bounded rank positive semidefinite matrix completions
new graph parameter bounded rank positive semidefinite matrix completions Optimization and Control
2012/4/23
The Gram dimension $\gd(G)$ of a graph $G$ is the smallest integer $k\ge 1$ such that any partial real symmetric matrix, whose entries are specified on the diagonal and at the off-diagonal positions c...
Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization
nonnegative matrix factorization algorithms multiplicative updates hierarchical alternating least squares
2011/9/21
Abstract: Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational ...
Conditional Gradient Algorithms for Rank-One Matrix Approximations with a Sparsity Constraint
Sparse Principal Component Analysis PCA Conditional Gradient Algorithms Sparse Eigenvalue Problems
2011/8/26
Abstract: The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine le...