Title :
Convex Optimization with Abstract Linear Operators
Author :
Steven Diamond;Stephen Boyd
Author_Institution :
Dept. of Comput. Sci. &
Abstract :
We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in the original problem. By representing linear functions in the transformation process not as matrices, but as graphs that encode composition of abstract linear operators, we arrive at a matrix-free cone program, i.e., one whose data matrix is represented by an abstract linear operator and its adjoint. This cone program can then be solved by a matrix-free cone solver. By combining the matrix-free modeling framework and cone solver, we obtain a general method for efficiently solving convex optimization problems involving fast linear transforms.
Keywords :
"Sparse matrices","Convex functions","Convolution","Transforms","Standards","Signal processing algorithms","Matrix converters"
Conference_Titel :
Computer Vision (ICCV), 2015 IEEE International Conference on
Electronic_ISBN :
2380-7504
DOI :
10.1109/ICCV.2015.84