Sparse Matrix Methods in Optimization

Optimization Methods for Sparse Matrix-Vector Multiplication

Sparsity: Optimization Framework for Sparse Matrix Kernels

Sparse matrix-vector multiplication is an important computational kernel that performs poorly on most modern processors due to a low compute-to-memory ratio and irregular memory access patterns. Optimization is difficult because of the complexity of cache-based memory systems and because performance is highly dependent on the nonzero structure of the matrix. The Sparsity system is designed to a...

Sparse Matrix Ordering Methods for Interior Point

The main cost of solving a linear programming problem using an interior point method is usually the cost of solving a series of sparse, symmetric linear systems of equations, AA T x = b. These systems are typically solved using a sparse direct method. The rst step in such a method is a reordering of the rows and columns of the matrix to reduce ll in the factor and/or reduce the required work. T...

Decomposition Methods for Sparse Matrix Nearness Problems

We discuss three types of sparse matrix nearness problems: given a sparse symmetric matrix, find the matrix with the same sparsity pattern that is closest to it in Frobenius norm and (1) is positive semidefinite, (2) has a positive semidefinite completion, or (3) has a Euclidean distance matrix completion. Several proximal splitting and decomposition algorithms for these problems are presented ...

Tensor Methods for Large, Sparse Unconstrained Optimization

Tensor methods for unconstrained optimization were rst introduced by Schn-abel and Chow SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate-size problems. The major contribution of this paper is the extension of these methods to large, sparse unconstrained optimization problems. This extension requires an entirely new way of solving the tensor model th...