Open Collections

CQ algorithms : theory, computations and nonconvex extensions

University of British Columbia

The split feasibility problem (SFP) is important due to its occurrence in signal processing and image reconstruction, with particular progress in intensity-modulated radiation therapy. Mathematically, it can be formulated as finding a point x∗ such that x∗ ∈ C and Ax∗ ∈ Q, where A is a bounded linear operator, C and Q are subsets of two Hilbert spaces H₁ and H₂ respectively. One particular algorithm for solving this problem is the CQ algorithm. In this thesis, previous work on CQ algorithm is presented and a new proof of convergence of the relaxed CQ algorithm is given. The CQ algorithm is shown to be a special case of the subgradient projection algorithm. The SFP is extended into two nonconvex cases. The first one is on S-subdifferentiable functions, and the other one is on prox-regular functions. The subgradient projection algorithm and CQ algorithm are proved to converge to a solution of the first and second case respectively.

Text

2014-08-26

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50178

Interdisciplinary Studies

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/